Use right angle congruence

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Presentation transcript:

Use right angle congruence EXAMPLE 1 Use right angle congruence Write a proof. GIVEN: AB BC , DC BC PROVE: B C STATEMENT REASONS 1. AB BC , DC BC 1. Given 2. B and C are right angles. 2. Definition of perpendicular lines 3. B C 3. Right Angles Congruence Theorem

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

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

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

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

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