1. Concept

2. 15  11 Corresponding Angles Postulate
Use Corresponding Angles Postulate
A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.
15  11 Corresponding Angles Postulate
m15 = m11 Definition of congruent angles
m15 = 51 Substitution
Answer: m15 = 51
Example 1

3. Use Corresponding Angles Postulate
B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.
15  11
15  16
11  16
m11 = m16
m16 = 51
Corresponding Angles Postulate
Substitution
Supplement Theorem
Definition of Congruent Angles
Substitution
Answer: m16 = 51
Example 1

4. A B C D A. In the figure, a || b and m18 = 42. Find m22. A. 42 B. 84
Example 1a

5. A B C D B. In the figure, a || b and m18 = 42. Find m25. A. 42 B. 84
Example 1b

6. Concept

7. Concept

8. Alternate Interior Angles Postulate
Use Theorems about Parallel Lines
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.
2  3
m2 = m3
125 = m3
Answer: m3 = 125
Alternate Interior Angles Postulate
Definition of congruent angles
Substitution
Example 2

9. FLOOR TILES The diagram represents the floor tiles in Michelle’s house
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.
A. 25
B. 55
C. 70
D. 125 A B C D
Example 2

10. A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
Find Values of Variables
A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
5  7
m5 = m7
2x – 10 = x + 15
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer: x = 25
Corresponding Angles Postulate
Definition of congruent angles
Substitution
Example 3

11. B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
Find Values of Variables
B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
8  6
m8 = m6
4y = m6
Corresponding Angles Postulate
Definition of congruent angles
Substitution
Example 3

12. Distributive Property
Find Values of Variables
m6 + m4 = 180
4y + 4(y – 25) = 180
4y + 4y – 100 = 180
8y = 280 Add 100 to each side.
y = 35 Divide each side by 8.
Supplement Theorem
Substitution
Distributive Property
Answer: y = 35
Example 3

13. A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.
A. x = 9
B. x = 12
C. x = 10
D. x = 14 A B C D
Example 3

14. B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y.
A. y = 14
B. y = 20
C. y = 16
D. y = 24 A B C D
Example 3

15. Concept