EXAMPLE 1 Use right angle congruence

GIVEN: AB BC , DC BC

PROVE: B C

Write a proof.

STATEMENT REASONS

1.Given

2.Definition of perpendicularlines

3.Right Angles CongruenceTheorem

2. B and C are right angles.

3. B C

1.AB BC , DC BC

EXAMPLE 2 Prove a case of Congruent Supplements Theorem

GIVEN: 1 and 2 are supplements.3 and 2 are supplements.

PROVE: 1 3

Prove that two angles supplementary to the same angle are congruent.

EXAMPLE 2 Prove a case of Congruent Supplements Theorem

STATEMENT REASONS

1.3 and 2 are supplements.1 and 2 are supplements. Given1.

2. m 1+ m 2 = 180°m 3+ m 2 = 180°

2. Definition of supplementary angles

Transitive Property of Equality

3.3.m 1 + m 2 = m 3 + m 2

4. m 1 = m 3

5. 1 3

Subtraction Property of Equality

4.

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?

2. Draw a diagram and write GIVEN and PROVE statements for a proof of each case of the Congruent Complements Theorem.

ANSWER

2 Steps

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.)