1. 2.72.7 Prove Angle Pair Relationships
Bell Thinger
Give a reason for each statement.
ANSWER Transitive Prop. of Eq.
ANSWER Def. of perpendicular
ANSWER Def. of segment congruence
1. If m 1 = 90º and m 2 = 90º, then m 1 = m 2.
2. If AB BC , then ABC is a right angle.┴
3. If FG RS, then FG = RS=

2. 2.7

3. 2.7Example 1
STATEMENTS REASONS
1.Given1. AB BC , DC BC
2.Definition of perpendicular
lines
2. B and C are right
angles.
Write a proof.
GIVEN: AB BC , DC BC
PROVE: B C
3.Right Angles Congruence
Theorem
3. B C

4. 2.7

5. 2.7Example 2
Prove that two angles supplementary to the same angle
are congruent.
GIVEN: 1 and 2 are supplements.
3 and 2 are supplements.
PROVE: 1 3

6. 2.7
STATEMENTS REASONS
Given1.
Example 2
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 Subtraction
Property of Equality
4.
5. 1 3 Definition of
congruent angles
5.
1 and 2 are supplements.1.
3 and 2 are supplements.

7. 2.7

8. 2.7Example 3
GIVEN: 5 and 7 are vertical angles.
PROVE: 5 7
Prove vertical angles are congruent.
STATEMENTS REASONS
5 and 7 are vertical angles.1. 1. Given
2. 5 and 6 are a linear pair.
6 and 7 are a linear pair.
2. Definition of linear
pair, as shown in the
diagram
3. 5 and 6 are supplementary.
6 and 7 are supplementary.
3. Linear Pair Postulate
4. 5 7 Congruent
Supplements Theorem
4.

9. 2.7Guided Practice
2. If m 1 = 112°, find m 2,
m 3, and m 4.
ANSWER m 2 = 68°
m 3 = 112°
m 4 = 68°
3. If m 2 = 67°, find m 1, m 3, and m 4.
ANSWER m 1 = 113°
m 3 = 113°
m 4 = 67°

10. 2.7Guided Practice
4. If m 4 = 71°, find m 1, m 2, and m 3.
ANSWER m 1 = 109°
m 2 = 71°
m 3 = 109°

11. 2.7Example 4
SOLUTION
Because TPQ and QPR form a linear pair, the sum
of their measures is 180.
The correct answer is B.
ANSWER

12. 2.7Example 5
Tell whether the proof is logically valid.
If it is not, explain how to change the
proof so that it is valid.
GIVEN: 1 is a right angle.
PROVE: 3 is a right angle.
STATEMENTS REASONS
1. 1 is a right angle. 1. Given
3. 3 is a right angle. 3. Right Angles
Congruence Theorem
2. 1 3 2. Vertical Angles
Congruence Theorem

13. 2.7
The proof is not logically valid. The Right Angles
Congruence Theorem does not let you conclude that
3 is a right angle. It just says that all right angles are
congruent.
Here is a way to complete the proof.
SOLUTION
Example 5

14. 2.7
REASONSSTATEMENTS
6. 3 is a right angle.
1. 1 is a right angle.
2. 1 3
1. Given
2. Vertical Angles
Congruence Theorem
3. Definition of congruent
angles
3. m 1 = m 3
4. m 1 = 90º
5. m 3 = 90º
4. Definition of right angle
5. Transitive Property of
Equality
6. Definition of right angle
Example 5

15. 2.7Guided Practice
5. Solve for x.
x = 49ANSWER
6. Find m TPS.
m TPS = 148°
ANSWER

16. 2.7Exit Slip
1. Give the reason for each step
Def. of linear pair
Given
PROVE : 1is supplementary to 4
GIVEN : 1 5
Substitution Prop. of Eq.
Def. of supplementary
Linear Pair Post .
Def. of supplementary
STATEMENTS REASONS
2. m 1 = m 5
3. 4 and are a linear pair.5
1. 1 5
4 and are supplementary .4. 5
m 4 + m 5 = 1805.
m 4 + m 1 = 1806.
7. 1 is supplementary to 4.
Def. of

17. 2.7
Homework
Pg 129-133
# 10, 14, 28, 37, 38