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55 Cards in this Set
- Front
- Back
Plane Postulates
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1. A line, a plane, and space contain infinite points.
2. For any two points there is exactly one line containing them 3. For any three noncollinear points there is exactly one plan containing them 4. If two points are in a plane, then the line containing them is in the plane 5. If two planes intersect, then they intersect at exactly one line |
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Segment Addition Postulate
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If Q is between P and R then PQ+QR= PR
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Angle Addition Postulate
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If F is in the interior of <CDE, then m<CDF + m<FDE = m<CDE
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Definition of Congruent
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Congruent segments are segments that have the same length. The same applies to angles with angle measure.
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Definition of Midpoint
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The midpoint of a segment is the point that divides the segment into two congruent segments.
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Definition of a bisector
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A bisector of a segment is the point, part of a line, or plane that divides the segment into two congruent segments. The bisector of an angle is a ray in the interior of the angle that divides the angle into two congruent angles.
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Midpoint Postulate/Angle Bisector Posulate
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A segment has exactly one midpoint. An angle has exactly one bisector.
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Definition of a triangle
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A triangle is a figure formed by three segments joining three non collinear points.
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Theorem about Angle and Segment Congruence
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Congruence of segments and angles is reflexive, symmetric, and substitutive.
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Definition of complementary angles
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Complementary angles are two angles whose measures have a sum of 90
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Definition of Supplementary Angles
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Supplementary angles are two angles whose measures have a sum of 180.
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Definition of Linear Pair
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A linear pair of angles is a pair of adjacent angles with the two noncommon sides on the same line.
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Linear Pair Posulate
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Two angles that form a linear pair are supplementary.
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Theorem about linear pairs
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The sum of the measures of the angles in a linear pair is 180.
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Vertical Angle Theorem
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If two angles are vertical angles, then they are congruent.
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Definition of Perpendicular Lines
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Perpendicular lines are two lines that intersect at right angles
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Theorem about perpendicular lines
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Through a given point on a line, there is exactly one line in the plane perpendicular to the given line.
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Definition of a Perpendicular Bisector
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A perpendicular bisector of a segment is a line, segment, ray, or plane that is perpendicular to the segment and bisects it.
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Information that May Be Assumed From a Diagram
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1. Straightness of lines
2. Betweenness of points 3. Collinearity of points on a line, coplanarity of points 4. Intersection of lines 5. Relative locations (interior, exterior, opposite) 6. Adjacency, nonadjacency of angles 7. Existence of the figures shown |
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Information that May Not be Assumed From a Diagram
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1. Congruence of segments or angles
2. Measures of segments or angles 3. Relative sizes of segments and angles 4. Midpoint of a segment or bisector of an angle 5. Perpendicular lines or right angles 6. Nonintersecting lines 7. Special types of figures |
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Theorem about right angles
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All right angles are congruent
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Midpoint Theorem
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The midpoint M of line segment AB divides AB so that AM=1/2 AB
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Angle Bisector Theorem
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If ray BD is the bisector of <ABC, then m<ABD=1/2 m<ABC
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Common Segment Theorem
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1. If AB is congruent to CD, then AC is congruent to BD
2. If AC is congruent to BD, then AB is congruent to CD |
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Theorem about congruent adjacent angles
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If two lines form congruent adjacent angles, then they are perpendicular
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Theorem about points and perpendicular lines
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Only one perpendicular line can be drawn from a point to a line
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Common Angle Theorem
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1. If <AOB is congruent to <COD, then <AOC is congruent to <BOD.
2. If <AOC is congruent to <BOD, then <AOB is congruent to <COD. |
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Congruent Complements Theorem
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Two angles that are complementary to the same angle (or to congruent angles) are congruent.
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Congruent Supplements Theorem
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Two angles that are supplementary to the same angle (or to congruent angles) are congruent.
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Methods of Proving an Angle a Right Angle
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1. Prove that it has a measure of 90.
2. Prove that it is formed by perpendicular lines. 3. Prove that it forms a linear pair with a right angle. |
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Definition of parallel planes
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Parallel planes are planes that do not intersect.
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Definition of parallel lines
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Parallel lines are coplanar and do not intersect.
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Definition of skew lines
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Skew lines are lines that are not coplanar and do not intersect.
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Theorem about parallel planes
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If two parallel planes are cut by a third plane, the lines of intersection are parallel.
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Definition of transversal
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A transversal is a line that intersects two coplanar lines in two different points. It forms eight angles.
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Definition of alternate interior angles
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Alternate interior angles are two nonadjacent interior angles on opposite sides of the transversal. There are two pairs of alternate interior angles.
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Definition of alternate exterior angles
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Alternate exterior angles are two nonadjacent exterior angles on opposite sides of the transversal. There are two pairs of alternate exterior angles.
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Definition of same-side interior angles
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Same-side interior angles are two interior angles on the same side of the transversal. There are two pairs of same-side interior angles.
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Definition of corresponding angles
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Corresponding angles are two non adjacent angles on the same side of the transversal such that one is an exterior angle and the other is an interior angle. There are four pairs of corresponding angles.
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Postulate about corresponding angles (know converse)
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If two parallel lines are cut by a transversal, then corresponding angles are congruent.
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Theorem about alternate interior angles (know converse)
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If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
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Theorem about alternate exterior angles (know converse)
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If two parallel lines are cut by a transversal then alternate exterior angles are congruent.
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Theorem about same-side interior angles (know converse)
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If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
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Theorem about perpendicular lines being parallel
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In a plane, two coplanar lines perpendicular to the same line are parallel.
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Theorem about transitive parallel lines
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Two lines parallel to a third lines are parallel to each other.
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Postulate about parallel lines and a point not on the line
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Given a line L and a point P not on line L, there exists one and only one line through P parallel to L.
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Angle Sum Theorem for Triangles
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The sum of the measures of the angles of a triangle is 180.
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Corollary about equilateral triangles
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The angles of an equiangular triangle each have a measure of 69.
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Corollary about right triangles
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The acute angles of a right triangle are complementary.
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The Exterior Angle Theorem
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The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
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Third Angle Theorem
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If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
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Polygon Names
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4-Quadrilateral
5-Pentagon 6-Hexagon 7-Heptagon 8-Octagon 9-Nonagon 10-Decagon |
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Theorem about polygon angle sum
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The sum of the measures of the angles of a convex polygon of n sides is ( n - 2 ) 180
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Corollary about regular polygons
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The measure of each angle of a regular polygon of n sides is ( n - 2 )( 180 ) / n
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Theorem about polygon exterior angle sum
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The sum of the measures of the exterior angles of a convex polygon is 360.
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