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CP Geometry 2.6 – Geometric Proofs Name: ___________ Date: _____ Block: ____ It is important to justify each logical step with a reason. You can use ____________ and ___________________, but they must be clear enough so that anyone who reads your proof will understand them. Example1: (a) Write a justification for each step, given that <A and <B are supplementary and m<A = 45°. 1. A and B are supplementary. m A = 45 2. m A + m B = 180 3. 45 + m B = 180 4. m B = 135 (b) Write a justification for each step, given that B is the midpoint of AC and AB 1. 2. 3. 4. EF. B is the midpoint of AC. AB BC AB EF BC EF A theorem is __________________________________________________ _____________________________________________________________________________. Linear Pair Theorem:_______________________________________________________ _____________________________________________________________________________. Hypothesis: Conclusion: Congruent Supplements Theorem: _________________________________________________ ______________________________________________________________________________ _____________________________________________________________________________. Hypothesis: Conclusion: A geometric proof begins with Given and Prove statements, which restate the hypothesis and conclusion of the conjecture. In a two-column proof, you list the steps of the proof in the ______________. You write the matching reason for each step in the _______________________. Example 2: Fill in the blanks to complete the two-column proof. Given: XY Prove: XY XY Statements 1. XY 2. XY = XY 3. XY XY Reasons ** Before beginning a proof, make sure to plan out your logic. Sometimes a plan will be given, but NOT always** Right Angle Congruence Theorem: _________________________________________________ ___________________________________________________________. Hypothesis: Conclusion: Congruent Complements Theorem:_________________________________________________ ______________________________________________________________________________ _____________________________________________________________________________. Hypothesis: Conclusion: Example 3: Given: 1 and 2 are supplementary, and 1 3 Prove: 3 and 2 are supplementary. Plan: Use the definitions of supplementary and congruent angles and substitution to show that m 3 + m 2 = 180°. By the definition of supplementary angles, 3 and 2 are supplementary