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Geometry Proof Postulates, Theorems, Definitions, & Pr
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Addition Property of Equality - ANSWERSIf A=B, then A+C=B+C. Subtraction Property of Equality - ANSWERSIf A=B, then A-C=B-C. Multiplication Property of Equality - ANSWERSIf A=B, then AC=BC. Division Property of Equality - ANSWERSIf A=B and C≠0, then A/C = B/C. Reflexive Property of Equality - ANSWERSFor any real number A, A=A. Symmetric Property of Equality - ANSWERSIf A=B, then B=A. Transitive Property of Equality - ANSWERSIf A=B, and B=C, then A=C. Substitution Property of Equality - ANSWERSIf A=B, then A can be substituted for B. Distributive Property of Equality - ANSWERSA(B+C)=AB+AC Definition of Congruent Angles - ANSWERSTwo angles that have the same measure. Right Angle Congruence Theorem - ANSWERSAll right angles are congruent. Congruent Supplements Theorem - ANSWERSIf two angles are supplementary to the same angles or congruent angles, then they are congruent. Congruent Complements Theorem - ANSWERSIf two angles are complementary to the same angles, then they are congruent. Linear Pair Postulate - ANSWERSIf two angles form a linear pair, then they are supplementary. Vertical Angles Theorem - ANSWERSVertical angles are congruent. Parallel Postulate - ANSWERSIf there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
Perpendicular Postulate - ANSWERSIf there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. Perpendicular Line Theorem #1 - ANSWERSIf two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. Perpendicular Line Theorem #2 - ANSWERSIf two sides of two adjacent acute angles are perpendicular, then the angles are complementary. Perpendicular Line Theorem #3 - ANSWERSIf two lines are perpendicular, then they intersect to form right angles. Corresponding Angles Postulate - ANSWERSIf parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Alternate Interior Angles Theorem - ANSWERSIf two parallel lines are cut by a transversal, then the alternate interior angles are congruent. Consecutive Interior Angles Theorem - ANSWERSIf two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary. Alternate Exterior Angles Theorem - ANSWERSIf two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. Perpendicular Transversal Theorem - ANSWERSIf a transversal is perpendicular to one of two parallel liens, then it is perpendicular to the other. Corresponding Angles Converse - ANSWERSIf two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. Alternate Interior Angles Converse - ANSWERSIf two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. Consecutive Interior Angles Converse - ANSWERSIf two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. Alternate Exterior Angles Converse - ANSWERSIf two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel.