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354 Cards in this Set
- Front
- Back
(n-2)180
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The sum of the measures of the angles of an n-gon.
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180
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The sum of the measures of the angles of a triangle.
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3 undefined terms
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point
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(n-2)180
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The sum of the measures of the angles of an n-gon.
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180
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The sum of the measures of the angles of a triangle.
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3 undefined terms
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point, line, plane
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360
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The sum of the measures of the internal angles of a quadrilateral.
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60 degrees
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The measure of each angle in an equiangular triangle
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AAS
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Two triangles are congruent if 2 sets of corresponding angles and one set on non-included sides are congruent.
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acute angle
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an angle whose measure is between 0 and 90 degrees
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acute angle
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an angle with measure btwn 0* and 90*
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Acute Triangle
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A triangle whose angles are less than 90 degrees.
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acute triangle
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a triangle with 3 acute angles
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Acute Triangle
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A triangle with 3 acute angles
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Acute Triangle
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A triangle with all acute angles
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acute triangle
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a triangle with all acute interior angles
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acute triangle
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a triangle with all sides acute
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Acute Triangles
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Triangles containing three acute angles
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Addition Property
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If a=b, the a+c=b+c
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Adjacent Angles
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2 coplanar angles with a common side, common vertex, and no common interior points
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adjacent angles
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two angles that share a common vertex and common ray and have interior points in common
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adjacent angles
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two angles with a common vertex and side but no common interior points
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adjacent angles
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two coplanar angles with a common side, a common vertex, and no common interior point
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adjacent arcs
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arcs of the same circle that have exactly one point in common
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adjacent arcs
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arcs on the same circle and have exactly one point in common
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adjacent sides
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2 sides of a triangle with a common vertex
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alternate exterior angles
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2 angles that are formed by 2 lines and a transversal and that lie outside the 2 lines on opposite sides of the transversal
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Alternate Exterior Angles
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Congruent when lines are parallel.
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alternate interior angles
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2 angles that are formed by 2 lines and a transversal and that lie between the 2 lines on opposite sides of the transversal
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alternate interior angles
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both on interior, opposite sides of transversal, non adjacent
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Alternate Interior Angles
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Congruent when lines are parallel.
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Alternate Interior Angles
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Non adjacent interior angles that lie in opposite sides of the transversal
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alternate interior angles
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nonadjacent interior angles that lie on opposite sides of the transversal
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altitude (prism)
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a perpendicular segment that joins the planes of the bases
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altitude of a parallelogram
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any segment perpendicular to the line containing the base drawn from the side opposite the base
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altitude of a triangle
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the perpendicular segment form a vertx to the line containing the opposite side
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altitude of an equilateral triangle
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h=½s√3
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altitude
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a segment perpendicular to the line containing that base drawn from the side opposite the base
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Altitude
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A special segment of a triangle that drops from a vertex of the triangle perpendicular to the opposite side
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altitude
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line segment from a vertex of a triangle perpendicular to the opposite side
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Altitude
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Segment from a vertex that is perpendicular to opposite side
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Altitude
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The segment extended from a vertex of a triangle,perpendicular to the opposite side
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Angle Addition Postulate
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m<AOB+m<BOC=m<AOC
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Angle Angle Side
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AAS or SAA
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angle bisector
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a ray that divides an angle into two adjacent angles that are congruent
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Angle Bisector
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A ray that divides an angle into two congruent coplanar angles
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angle bisector
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a ray that divides an angle into two congruent parts
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angle bisector
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a ray, segment, or line that divides an angle into two congruent angles
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Angle Bisector
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A special segment of a triangle that cuts an angle of the triangle into two equal parts
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Angle Bisector
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Bisects an angle into 2 congruent angles
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angle of depression
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the angle formed by a horizontal line and the line of sight to an object below the horizontal line
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angle of elevation
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the angle formed by a horizontal line and the line of sight to an object above the horizontal line
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Angle Side Angle
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ASA
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angle
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consists of two different rays that have the same initail point
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angle
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formed by two rays with the same endpoint
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angle
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the union of 2 rays that have a common endpoint called a vertex
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angle
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two rays that share a common end point
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any two points are collinear
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axiom
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apothem of a regular polygon
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the distance from the center to a side
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apothem
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a segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon
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arc length
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a fraction of the circumference
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arc
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part of the circle
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area of a circle
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A=πr²
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area of a parallelogram
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A=bh or A=ab(sin(C))
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area of a rectangle
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A=ab
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area of a right triangle
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A=½(ab)
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area of a semicircle
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A=½πr²
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area of a sphere
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4 pi r squared
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area of a square
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A=s² or A=½d²
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area of a trapezoid
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A=½h(B+b)
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area of a triangle
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A=½(bh) or A=.5(ab)sin(C)
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area of an equilateral triangle
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A=¼s²√3
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ASA
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Two triangles are congruent if 2 sets of corresponding angles and their included side are congruent.
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Axiom
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a mathematical statement which we except as true because no counter example exists
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axiom
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a statement that we can accept as true
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base angle
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an angle of an isosceles triangle opposite one of the equal sides
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base angle
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two angles that share a base of a trapezoid
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Base Angles Converse
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If two angles of a triangle are congruent, then the sides opposite to them are congruent
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Base Angles Theorem
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If two sides of a triangle are congruent, then the angles opposite to them are congruent
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base angles
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other angles (isosceles triangle)
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base of a parallelogram
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any of its sides
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base of a parallelogram
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any side of a parallelogram
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base of a triangle
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any side of a triangle
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base
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(no definition)
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base
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the third side
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bases
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parallel faces
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between
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a point that lies on the same line and "between" two other points
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BiConditional
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p<->q(Conditional must be true & converse must be true) (if and only if)
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biconditional
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the conjunction of p->q and q->p in words: if and only if
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biconditional
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when a conditional and its converse are true and you combine them, the joining of the conditional and converse (if p, then q and if q the p) (P<->q)
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bisect
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to divide into two congruent parts
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center of a circle
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a point equidistant from any point on the circumference of a circle
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center of a regular polygon
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the center of the circumscribed circle in a regular polygon
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center of a sphere
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a set point in space where all points of a sphere are equidistant from it
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center
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the given point
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central angle (circle)
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angle whose vertex is the center of the circle
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central angle (regular polygon)
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angle formed by two consecutive radii
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central angle
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an angle formed by two consecutive radii
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central angle
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vertex is center, sides are radii
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Centroid
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Point of Concurrency for Median
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centroid
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point of concurrency of the three medians of a triangle
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Centroid
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The point formed by the medians
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centroid
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the point of congruency of the medians, in a triangle
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chord
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a segment whose endpoints are on a circle
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chord
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a segment whose endpoints are on the circle
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chord
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a segment with endpoints on the circle
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circle
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the set of all points equidistant form a given point on a plane
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circle
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the set of all points in a plane that are a given distance
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circle
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the set of all points in a plane that are a given distance from a given point
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circumcenter of the triangle
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the point of concurrency of the perpendicular bisectors of a triangle
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Circumcenter
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Point of Concurrency for Perpendicular Bisector
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circumcenter
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the point of concurrency of the three perpendicular bisectors of the sides of a triangle
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circumference of a sphere
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the circumference of any great circle of the sphere
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circumference of circle
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the distance around a circle
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circumference or a circle
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C=πd or C=2πr
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circumference
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2 (pi) r
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circumference
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the distance around the circle
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circumscribed about
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a circle is __ __ a polygon if the vertices of the polygon are on the circle
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circumscribed about
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when the vertices of the polygon are on the circle
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circumscribed about
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when the vertices of the polygon are on the circle
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collinear points
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points that lie on the same line
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collinear
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a set of points that lie on a common line
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collinear
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points that are on the same line
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Collinear
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Points that lie on the same line
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collinear
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two or more points that lie on the same line
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compass
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geometric tool used to draw circles and archs
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Complementary Angles
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2 angles that add up to the sum of 90
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complementary angles
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2 angles whose measures add up to 90 degrees
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complementary angles
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two angles whose measures have the sum of 90
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complementary angles
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two angles whose measures have the sum of 90*
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composite space figure
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a three-dimensional figure that is the combination of two or more simpler figures
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composition
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a combination of two or more transformations
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concave polygon
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has at least one diagonal with points outside the polygon
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Concave Polygon
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Polygon that has at least one diagonal with points outside the polygon
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concentric circles
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circles that lie in the same plane and have the same center
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concentric circles
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circles that lie in the same plane and have the same center
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conclusion
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the part following "then", logical inference
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Concurrent Lines
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3 or more lines that intersect at the same point. ** The point is called the Point OF Concurrency**
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concurrent
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when three or more lines intersect in one point
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conditional
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a compound statement of the form "if p, then q" p is called the hypothesis and q is called the conclusion
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Conditional
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an if-then statement.
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conditional
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another name for an if-then statement
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cone
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"pointed like a pyramid", but its base is a circle
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cone
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a 3D figure with a circular base, a vertex not in the plane of the circle, and a curved lateral surface. it is NOT a polyhedron
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Congruence Transformation
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Either a translation, reflection, or rotation
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Congruent Angle
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Angles with the same measure
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congruent angles
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angles that have the same measure
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congruent angles
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angles with the same measure
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congruent angles
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two angles that have the same measure
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congruent arcs
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arcs that have the same measure and are in the same circle or congruent circles
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congruent arcs
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arcs that have the same measure and are in the same circle or in congruent circles
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congruent circles
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circles whose radii are congruent
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congruent circles
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circles whose radii are congruent
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Congruent Polygon
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Polygon with congruent corresponding parts-matching sides and angles
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congruent polygons
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have congruent corresponding parts
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Congruent Polygons
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Two geometric figures that are congruent if they have exactly the same size and shape
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Congruent Segments
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Segments with the same length
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congruent segments
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two segments that have the same measure
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congruent segments
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two segments with the same length
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congruent triangles
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2 triangles are congruent if and only if all pairs of corresponding sides and angles are congruent
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conjecture
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a conclusion you reach using inductive reasoning
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conjecture
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an unproven statement that is passed on observations
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conjunction
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a compound statement formed by joining two statements using "and"
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consecutive angles
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angles of a polygon that share a side (parallelogram-consecutive angles are supplementary)
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consecutive interior angles
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2 angles that are formed by 2 lines and a transversal and that lie between the 2 lines on the same side of the transversal
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construction
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use a straight edge and a compass to draw a geometric figure
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contrapositive
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a statement that negates the hypothesis and the conclusion and switches their orders of the original statement
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contrapositive
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Given: If P then Q. Therefore if not Q then not P
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Contrapositive
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~q -> ~p
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converse
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a statement that switches the order of the hypothesis and the conclusion of the original statement
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Converse
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q -> p (Conclusion to Hypothesis)
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converse
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switches the hypothesis and the conclusion
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convex polygon
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has no diagonal with points outside the polygon
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Convex Polygon
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Polygon that has no diagonal with points outside the polygon
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Coordinate Notation
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When figures are drawn on a coordinate plane, you can use this to describe a translation or reflection
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coordinate
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the real number that corresponds to a point on a line
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coplanar points
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points that lie on the same plane
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Coplanar
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Points and lines that is on the same plane
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coplanar
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points on the same plane
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coplanar
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two or more points on the same plane
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Corollary to Base Angles Converse
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If a triangle is equiangular, then it is equilateral
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Corollary to Base Angles Theorem
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If a triangle is equilateral, then it is equiangular
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Corollary to Triangle Sum Theorem
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The acute angles of a right triangle are complementary
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corollary
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a statement that follows immediately form a theorem
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Corollary
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A statement that follows immediately from a theorem
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Corresponding Angles
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Congruent when lines are parallel.
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corresponding angles
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lie on the same side of the transversal, separated by two lines, same side on each line
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Corresponding Angles
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Non adjacent angles, only one interior , that lie on the same side of the transversal
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corresponding angles
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two angles that are formed by two lines and a transversal and occupy corresponding positions
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cosine
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the ratio of the adjacent leg over the hypotenuse of an angle
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counter example
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an example that shows a conjecture is false
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Counter-example
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Statement that proves the conditional is false(MUST be 1). True for hypothesis AND 2) FALSE for conclusion
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counterexample
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an example for which the conjecture is incorrect
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CPCTC
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Corresponding Parts of Congruent Triangles are Congruent.
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CPCTC
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corresponding parts of congruent triangles are congruent
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cross section
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the intersection of a solid and a plane
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cross section
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the intersection of a solid and a plane
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cube
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a polyhedron with six faces, each of which is a square
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cylinder
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a 3d figure with 2 congruent circular bases that lie in parallel planes
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Decagon
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Polygon with 10 sides
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deductive reasoning
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a conclusion made by using a series of truth statements and laws of reasoning
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definition
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uses known words to describe a new word
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degree
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1/360 of a complete rotation
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degrees
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a way to measure an angle
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diagonal of a rectangular box
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square root L2+w2+h2
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diagonal of a square
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d=s√2
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Diagonal
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Segment that connects 2 nonconsecutive vertices
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diameter (circle)
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a segment that contains the center of a circle and whose endpoints are on the circle
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diameter of a sphere
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a segment passing through the center, with endpoints on the sphere
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diameter
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a segment that contains the center of the circle and whose endpoints are on the circle
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diameter
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chord that passes through the center of the circle
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dilation
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transformation whose image and object are similar. NOT an isometry., The transformation of a figure to a similar figure of different size.
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disjunction
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a compound statement formed by joining two statements using "or"
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distance formula
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-
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distance from a point to a line
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the length of the perpendicular segment from the point to the line
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distance
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the distance between 2 points
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Distributive Property
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a(b+c) = ab +ac
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Division Property
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If a=b,then a/c=b/c
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Dodecagon
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Polygon with 12 sides
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edge
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a segment that is formed by the intersection of two faces
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edge
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the intersection of the faces of the polyhedron
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enlargement
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gets larger
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equiangular polygon
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a polygon whose angles are all congruent
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Equiangular Polygon
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all congruent ANGLES
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Equiangular Triangle
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A triangle whose angles are congruent.
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equiangular triangle
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a triangle with 3 congruent angles.
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Equiangular Triangle
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A triangle with 3 congruent angles
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Equiangular Triangle
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A triangle with equal angles
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Equilangular Triangles
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Triangle with all congruent angles
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equilateral polygon
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a polygon whose sides are all congruent
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Equilateral Polygons
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all congruent SIDES
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Equilateral Triangle
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A triangle whose sides are congruent.
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equilateral triangle
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a triangle with 3 congruent sides
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Equilateral Triangle
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A triangle with 3 congruent sides
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Equilateral Triangle
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A triangle with all sides congruent, a three-sided regular polygon
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Equlilateral Triangles
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Triangle with all congruent sides
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Exterior Angle Theorem
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The exterior angle of a triangle is equal to the sum of its remote interior angles.
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Exterior Angle Theorem
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The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles
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Exterior angle
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upon extending a side of a triangle, the angle adjacent to interior angle of triangle
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Exterior Angles
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Angle formed by a side and an exterior of an adjacent side
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exterior angles
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angles that are adjacent to the interior angles
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Exterior Angles
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The angles that form linear pairs with the interior angles
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exterior of an angle
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all points not on the angle or in its interior
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face
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each polygon
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face
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the surfaces of a polyhedron
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foundation drawing
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shows the base of a structure and the height of each part
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foundation drawing
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shows the base of a structure and the height of each part
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geometric mean
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the number (x) such that a/x = x/b, where a,b, and x are positive numbers
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geometric mean
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the number x such that a/x = x/b, where a and b are both positive numbers, x = (square root of AB)
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geometric probability
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a probability that uses a geometric model in which points represent outocmes
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Geometry
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The Study Of Earth
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glide reflection
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the composition of a glide (translation) and a reflection in a line parallel to the glide vector
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glide reflectional symmetry
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a glide reflection maps the tessellation onto itself
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golden ratio
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1.618 : 1
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golden rectangle
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a rectangle that can be divided into a square and a rectangle that is similar the the origional retangle
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great circle
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the intersection of a sphere and the plane containing the center of the sphere. divides a sphere into 2 hemispheres.
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great circle
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when the center of the circle is also the center of the sphere
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height (prism)
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the length of an altitude
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height of a parallelogram
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the length of a parallelogram's altitude
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height of a trapezoid
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the length of a trapezoid
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height of a triangle
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the length of the altitude drawn to the line containing that base
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height of prism
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length of the altitude
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height
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the length of the altitude
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hemisphere
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half of a great circle
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Hexagon
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Polygon with 6 sides
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HL
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2 right trianles are congruent if their hypotenuses and a set of corresponding legs are congruent.
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Hypotenuse Leg Theorem
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HL
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hypotenuse
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c²=a²+b²
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hypotenuse
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in aright triangle the side opposite the right angle
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hypotenuse
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the longest side in a right triangle
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Hypotenuse
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The longest side of a right triangle
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hypothesis
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the part following "if"
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identity
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an equation that is true for all allowed values of the variable
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image
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resulting figure
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incenter of the triangle
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the point of congruency of the angle bisectors of a triangle
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Incenter
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Point of Concurrency for Angle Bisector
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incenter
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the point of concurrency of the angle bisectors of all angles in the triangle
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included angle
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given 2 sides in a triangle, the included angle is the angle whose rays contain the two sides
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included side
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given 2 angles in a triangle, the included side is the side whose endpoints are the vertices of the angles
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indirect measurement
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a way of measuring things that are difficult to measure directly
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inductive reasoning
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a general truth that we conclude by looking at a series of examples
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inductive reasoning
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process that includes looking for patterns and making conjectures
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inductive reasoning
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reasoning based on patterns you observe
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initial point
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where the vector starts
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inscribed angle
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an angle in a circle where the vertex of the angle is on the circle and the sides are chords of the circle
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inscribed angle
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when the vertex of the angle is on the circle and the sides of the angle are chords of the circle
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inscribed in
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sides of the polygon are tangent to the circle
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inscribed in
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when the sides of the polygon are tangent to the circle
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intercepted arc
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an arc of a circle having endpoints on the sides of an inscribed angle, and its other pints in the interior of the angle
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intercepted arc
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an arc of a circle having endpoints on the sides of an inscribed angle, and its other points in the interior of the angle
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interior angles
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the 3 original angles of a triangle
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Interior Angles
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The original angles
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interior of an angle
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all points btwn the points that lie on each sides of the angles
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intersect
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to have one or more points in common
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intersection
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the set of points that two or more geometric figures have in common
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intersection
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two geometric figures points in common
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inverse
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a statement that negates both the hypothesis and the conclusion of the original statement
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inverse
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negates both the hypothesis and the conclusion
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Inverse
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~p -> ~q (~ = not)
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isometric drawing
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shows a corner view of a figure
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isometry
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a transformation in which the pre-image and image are congruent
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Isosceles Trapezoid
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A quadrilateral with exactly one pair of opposite sides parallel and whose nonparallel sides are congruent
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isosceles trapezoid
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nonparallel opposite sides are congruent
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Isosceles Triangle Theorem
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The base angles of an isosceles triangle are congruent
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Isosceles Triangle
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A triangle that has at least two sides congruent.
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Isosceles Triangle
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A triangle with 2 (at least) congruent sides
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isosceles triangle
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a triangle with at least 2 congruent sides
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Isosceles Triangle
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A triangle with at least two congruent sides
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isosceles triangle
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a triangle with at least two congruent sides
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isosceles triangle
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triangle with two congruent segments
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Isosceles Triangles
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Triangle with at least 2 sides
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Kite
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A quadrilateral with 2 pairs of adjacent sides congruent and no congruent opposite sides
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kite
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quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent
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LA of cone
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pi r l (slant height)
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LA of cylinder
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2 pi r h
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LA of prism
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ph
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LA of pyramid
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1/2 pl (l=slant height)
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lateral area
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the sum of the areas of the lateral faces
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lateral area
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the sum of the areas of the lateral faces or the curved surface of a 3d figure.
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lateral faces
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the faces that are not the base of a parallelogram
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lateral faces
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the other faces
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legs
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the congruent sides of an isosceles triangle
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legs
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the sides of a triangle
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length of a semicircle
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L=½πd or L=πr
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length of hyotenuse
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c=√a²+b²
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line segment
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part of a line with two endpoints
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line segment
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parts of a line that consists of 2 points, called endpoints, and all points on the line that are btwn the endpoint
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line segment
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point of a line consisting of two points on the line called endpoints and all the points between them
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line symmetry
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reflectional symmetry (like a butterfly)
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line
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(undefined) a set of points in a plane that satisfy the same linear relationship (extend in opposite directions without end)
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line
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a line extends in one dimension
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Line
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A Series of points that extend in opposite directions without a end
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line
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a set of points that extends forever in 2 opposite directions
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line
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an infinitely long infinitely thin straight path
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linear pair
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two adjacent angles that form a straight line
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linear pair
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two adjacent angles whose noncommonsides are opposite rays
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linear pair
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two angles form this if and only if they are adjacent angles whose noncommon sides are opposite rays
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locus
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a set of points, all of which meet a stated condition
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logically equivalent
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two statements whose truth value are always the same
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Longest Side
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The side of the triangle that is opposite the largest angle
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magnitude
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size
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major arc
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an arc of a circle larger than a semicircle
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major arc
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an arc that is larger than a semicircle
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mean proportional
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a proportion whose means are equal
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median of a triangle (1)
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a segment whose endpoints are a vertex and the midpoint of the opposite side
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Median
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A segment whose endpoints are the vertex and the midpoint of the opposite side
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Median
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A special segment of a triangle that connects a vertex of the triangle to the midpoint of the opposite side
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median
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line segment from a vertex of a triangle to the midpoint of the opposite side
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Median
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Segment from a vertex to the midpoint of opposite side
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Mid segment of a trapezoid
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A segment that connects the midpoints of nonparallel sides of a trapezoid
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Mid segment of a Triangle
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A segment connecting the midpoints of 2 sides
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Mid-segment
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A special segment of a triangle that connects the midpoints of two sides of the triangle
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midpoint formula
|
-
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midpoint
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a point on a line segment that cuts it into two congruent segments
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