1. Give a reason for each statement.
1. If m = 90º and m = 90º, then m = m
ANSWER
(Transitive Prop. of Eq.)
2. If AB BC , then ABC is a right angle. ┴
ANSWER
(Def. of perpendicular)

2. Give a reason for each statement.
3. If FG RS, then FG = RS =
ANSWER
(Def. of segment congruence)

3. 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

4. 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

5. 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.

6. 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.

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

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

9. EXAMPLE 3
Prove the Vertical Angles Congruence Theorem
Prove vertical angles are congruent.
GIVEN:
5 and are vertical angles.
PROVE:
∠ 5 ∠ 7

10. Prove the Vertical Angles Congruence Theorem
EXAMPLE 3
Prove the Vertical Angles Congruence Theorem
STATEMENT
REASONS
5 and are vertical angles. 1. 1.
Given 2.
5 and are a linear pair.
6 and are a linear pair. 2.
Definition of linear pair, as shown in the diagram 3.
5 and are supplementary.
6 and are supplementary. 3.
Linear Pair Postulate 4.
∠ 5 ∠
Congruent Supplements Theorem 4.

11. GUIDED PRACTICE
for Example 3
In Exercises 3–5, use the diagram.
3. If m = 112°, find m 2, m 3, and m
ANSWER
m = 68°
m = 112°
m = 68°

12. GUIDED PRACTICE
for Example 3
4. If m = 67°, find m 1, m 3, and m
ANSWER
m = 113°
m = 113°
m = 67°
5. If m = 71°, find m 1, m 2, and m
ANSWER
m = 109°
m = 71°
m = 109°

13. GUIDED PRACTICE
for Example 3
6. Which previously proven theorem is used in Example 3 as a reason?
Congruent Supplements Theorem
ANSWER

14. EXAMPLE 4
Standardized Test Practice
SOLUTION
Because TPQ and QPR form a linear pair, the sum of their measures is 180.
The correct answer is B.
ANSWER

15. GUIDED PRACTICE
for Example 4
Use the diagram in Example 4.
7. Solve for x.
x = 49
ANSWER

16. GUIDED PRACTICE
for Example 4
Use the diagram in Example 4.
8. Find m TPS.
m TPS = 148°
ANSWER

17. Daily Homework Quiz 1.
Give the reason for each step
GIVEN : 1 5
PROVE : 1
is supplementary to 4
Statements (Reasons) 1. 1 5
ANSWER
(Given) 2.
m 1 = m 5
ANSWER
(Def. of ) 3.
4 and are a linear pair. 5
ANSWER
(Def. of linear pair )

18. Daily Homework Quiz 4.
4 and are supplementary . 5
ANSWER
(Linear Pair Post .) 5.
m m = 180
ANSWER
(Def. of supplementary ) 6.
m m = 180
ANSWER
(Substitution Prop. of Eq.) 7.
1 is supplementary to
ANSWER
(Def. of supplementary )