1. 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

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

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

4. 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.

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

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