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87 Cards in this Set
- Front
- Back
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If a point is on the perpendicular bisector of a segment then
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the point is equidistant from both endpoints of the segment
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If a point is equidistant from both endpoints on segment then
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it is on the perpendicular bisector
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If a point is on the bisector of and angle then
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it is equidistant from the two sides of the angle
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The Perpendicular bisector s of a triangle intersect at a point that is
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equidistant from the vertices of the triangle
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The angle bisectors of a triangle intersect at a point that is
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equidistant form the sides of the triangle.
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The Medians of a triangle intersect at a point that is
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two thirds of the distance from each vertex to the midpoint of the opposite side
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The lines containing the altitudes of a triangle are
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congruent
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The segment connecting the midpoints of two sides of a triangle
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is parallel to the third side and half as long.
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If one side of a triangle is longer than another side then
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the angle opposite of the longer side is larger than the angle opposite the shorter side
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If one angle is larger than another angle the segment opposite the larger angle is
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larger than the segment opposite the smaller angle.
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The measure of an exterior angle of a triangle is greater than the measure of
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the two nonadjacent interior angles
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The Sum of the lengths of any two sides of a triangle is greater than
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the length of the third side
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If two sides of one triangle are congruent to two sides of another triangle and the included angle of the second and the third side of the first
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is longer than the third side of the second
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If two sides of one triangle are congruent to two sides of another triangle and the third side of the first is longer than the third of the second
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then the included angle of the first is larger than the included angle of the second
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Polygon is a plane figure that meets the following conditions
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It is formed by three or more segments called sides
Each sides intersects with exactly two other sides |
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Each endpoint in a polygon is a
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Vertex
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Equilateral means all sides are
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Congruent
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Equiangular means all angles are
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Congruent
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Regular means that a polygon is both
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equilateral and equiangular
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Parallelograms are quadrilaterals that have
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2 pairs of parallel sides
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Parallelograms opposite sides are
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Congruent
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Parallelograms opposite angles are
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Congruent
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Parallelograms consecutive angles are
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supplementary
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Parallelograms diagonals
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bisect each other
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Rhombuses are
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Parallelograms with 4 congruent sides
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Rectangles are
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Parallelograms with 4 right angles
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Squares are
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are Parallelograms with4 congruent sides and 4 right angles
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A Parallelogram is a rhombus if and only if
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it’s diagonals are perpendicular
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A Parallelogram is a rhombus if and only if
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if each diagonal bisects a pair of opposite angles
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A Parallelogram is a rectangle if and only if
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its diagonals are congruent
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If a trapezoid is isosceles then
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each pair of base angles is congruent
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If a trapezoid has a pair of congruent base angles then
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it is an isosceles trapezoid
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A trapezoid is isosceles if and only if
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it’s diagonals are congruent
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The Midsegment of a trapezoid is parallel to
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each base and is half of the sum of the bases lengths.
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If a quadrilateral is a kite then
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its diagonals are perpendicular
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If a quadrilateral is a kite then
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exactly one pair of opposite angles are congruent
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The area of a square is
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a side squared
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If two polygons are congruent then they
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have the same area
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Area of a rectangle=
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base times height
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Area of a parallelogram is
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base times height
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The area of a triangle is
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½ base times height
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The area of a trapezoid is
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½ h(b1+b2)
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The area of a kite is
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½ the product of the diagonals
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The area of a Rhombus is
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½ the product of the diagonals
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Ratio a to b is written as
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a/b or a:b
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In a ration the quotient cannot be
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zero
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a/b=c/d then
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ad=bc
b/a=d/c a and d are extremes b and c are means |
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If two polygons are similar then the ratio between their perimeters is
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equal to their corresponding sides
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If two polygons are similar then their angles
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are the same
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Angle angle postulate
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If two angles of one triangle are congruent to two angles of another triangle then the two triangles are similar.
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SIDE SIDE SIDE Postulate
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If the lengths of two triangles are proportional then the triangles are similar.
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Side angle Side Postulate
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If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional then the triangles are similar.
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If a line parallel to one side of a triangle intersects the other two sides then
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it divides the two sides proportionally
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If three lines intersect two transversals then
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they divide the transversals proportionally
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If a ray bisects an angle of a triangle then
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it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
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If the altitude is drawn to the hypotenuse of a right triangle then
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the two triangles formed are similar to the original triangle and to each other
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In a right triangle the altitude from the right angle divides the hypotenuse into two segments. What is the geometric mean
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The geometric mean of these two segments is the length of the altitude.
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In a right Triangle the square of the length of the hypotenuse is equal to
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the sum of the squares of the lengths of the legs.
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If the square of the hypotenuse is less than the sum of the squares of the other two sides then
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the triangle is acute
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If the square of the hypotenuse is greater than the sum of the squares of the other two sides then
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the triangle is obtuse
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In a 45 45 90 tiangle the hypotenuse is
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√2 times as long as each leg
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In a 60 30 90 the hypotenuse and longer leg is
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2 times as long as the shorter leg and the longer leg is √3 times as long as the shorter leg
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If sinA =x then
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sin-1x =m angle A
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If tanA =x then
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tan-1x =m angle A
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If cosA =x then
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cos-1x =m angle A
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casdf
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asdfasdf
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Center:
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The exact middle of a circle
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Radius
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The distance from the circle to the center. If 2 circles have the same radius then they are congruent
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Diameter
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The distance across the circle through the center. It equals 2 times the radius.
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Chord
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A segment whose endpoints are points on the circle.
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Secant
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A line that intersects a circle in two points
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Tangent
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a line that intersects with the circle at just one point
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Minor arcs
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<180
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Major arcs
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>180
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Semicircles
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=180
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If an angle is inscribed in a circle then its measure is
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half the measure of its intercepted arc.
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If two inscribed angles of a circle intercept the same arc then the angles
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are congruent
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If a right triangle is inscribed in a circle then the hypotenuse is
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is a diameter of the circle
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A quadrilateral can be inscribed in a circle if and only if its
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opposite angles are supplementary.
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If a tangent and a chord intersect at a point on a circle then the measure of each angle formed is
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one half the measure of its intercepted arc
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If two chords intersect in the interior of a circle then the product of the lengths of the segments of one chord is equal to
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the product of the lengths of the segments of the other chord
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If two secant segments share the same endpoint outside a circle then the product of the length of one secant segment and the length of its external segment equals
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the product of the length of the other secant segment and the length of its external segment.
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If a secant segment and a tangent segment share an endpoint outside a circle then the product of the lengths of the secant segment and the lengths of its external segment equals
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the square of the length of the tangent segment.
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The circumference of a circle is
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is c=pi D or 2 pi r
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In a circle the ration of the length of a given arc to the circumference is equal to the
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ration of the measure of the arc to 360
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The Area of a circle is
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pi time the square of the radius
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The ratio of the area of a sector of a circle to the area of the circle is equal to the measure of
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the intercepted arc to 360.
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