Holt McDougal Geometry 2-6 Geometric Proof 2-6 Geometric Proof Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry

2-6 Geometric Proof Warm Up Determine whether each statement is true or false. If false, give a counterexample. 1. It two angles are complementary, then they are not congruent. 2. If two angles are congruent to the same angle, then they are congruent to each other. 3. Supplementary angles are congruent. false; 45° and 45° true false; 60° and 120°

Holt McDougal Geometry 2-6 Geometric Proof Write two-column proofs. Prove geometric theorems by using deductive reasoning. Objectives

Holt McDougal Geometry 2-6 Geometric Proof Write a justification for each step, given that A and B are supplementary and mA = 45°. Example 1: Writing Justifications 1. A and B are supplementary. mA = 45° Given information 2. mA + mB = 180° Def. of supp s 3. 45° + mB = 180° Subst. Prop of = Steps 1, 2 4. mB = 135° Subtr. Prop of =

Holt McDougal Geometry 2-6 Geometric Proof A theorem is any statement that you can prove. Once you have proven a theorem, you can use it as a reason in later proofs.

Holt McDougal Geometry 2-6 Geometric Proof

Holt McDougal Geometry 2-6 Geometric Proof

Holt McDougal Geometry 2-6 Geometric Proof

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Holt McDougal Geometry 2-6 Geometric Proof Fill in the blanks to complete the two-column proof. Given: XY Prove: XY  XY Example 2: Completing a Two-Column Proof StatementsReasons 1.1. Given 2. XY = XY Def. of  segs. Reflex. Prop. of = 

Holt McDougal Geometry 2-6 Geometric Proof Check It Out! Example 2 Fill in the blanks to complete a two-column proof of one case of the Congruent Supplements Theorem. Given: 1 and 2 are supplementary, and 2 and 3 are supplementary. Prove: 1  3 Proof: a.1 and 2 are supp., and 2 and 3 are supp. b. m1 + m2 = m2 + m3 c. Subtr. Prop. of = d.  1   3

Holt McDougal Geometry 2-6 Geometric Proof Use the given plan to write a two-column proof. Example 3: Writing a Two-Column Proof from a Plan 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.

Holt McDougal Geometry 2-6 Geometric Proof Example 3 Continued StatementsReasons 1 and 2 are supplementary. 1  3 Given m1 + m2 = 180°Def. of supp. s m1 = m3 m3 + m2 = 180° 3 and 2 are supplementary Def. of  s Subst. Def. of supp. s