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Geometry Proofs: Congruent Angles Explanation

Learn how to prove angles congruent using geometry theorems and properties in two examples. Understand supplementary angles, right angle congruence, and the Transitive Property of Equality. Step-by-step guidance provided for practice proofs.

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Geometry Proofs: Congruent Angles Explanation

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  1. Write a proof. ABBC, DCBC GIVEN: BC PROVE: REASONS STATEMENT 1. 1. ABBC, DCBC Given 2. 2. Definition of perpendicular lines Band Care right angles. 3. BC 3. Right Angles Congruence Theorem EXAMPLE 1 Use right angle congruence

  2. Prove that two angles supplementary to the same angle are congruent. GIVEN: 1 and 2 are supplements. 3 and 2 are supplements. • 3 PROVE: EXAMPLE 2 Prove a case of Congruent Supplements Theorem

  3. REASONS STATEMENT 1. 1. 1 and 2 are supplements. Given 3 and 2 are supplements. 2. 2. m1+m2= 180° Definition of supplementary angles m3+m2= 180° 3. m 3 +m 2 3. m 1 +m 2 = Transitive Property of Equality 4. m1=m3 4. Subtraction Property of Equality 5. • 3 5. Definition of congruent angles EXAMPLE 2 Prove a case of Congruent Supplements Theorem

  4. ANSWER 2 Steps for Examples 1 and 2 GUIDED PRACTICE 1. How many steps do you save in the proof in Example 1 by using the Right Angles Congruence Theorem? 2. Draw a diagram and write GIVEN and PROVE statements for a proof of each case of the Congruent Complements Theorem.

  5. ANSWER Write a proof. Given: 1 and 3 are complements; 3 and 5 are complements. Prove:∠ 1 5 for Examples 1 and 2 GUIDED PRACTICE

  6. Statements (Reasons) 1.1 and 3 are complements; 3 and 5 are complements. (Given) 2.∠ 1 5 Congruent Complements Theorem. for Examples 1 and 2 GUIDED PRACTICE

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