1. Ch 4.3 Transversals and Corresponding Angles
Transversals & Corresponding Angles
Ch 4.3 Transversals and Corresponding Angles
Learning Target:
I will be able to use theorems to determine the relationships between specific pairs of angles and to use algebra to find angle measurements
Standard 7.0
Students prove and use theorems involving the properties of parallel lines cut by a transversal.

2. Ch 4.3
Transversals & Corresponding Angles
Postulate 4-1
Concept

3. Ch 4.3
Transversals & Corresponding Angles
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

4. Ch 4.3
Transversals & Corresponding Angles
Use Corresponding Angles Postulate
B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.
16  15 Vertical Angles Theorem
15  11 Corresponding Angles Postulate
16  11 Transitive Property ()
m16 = m11 Definition of congruent angles
m16 = 51 Substitution
Answer: m16 = 51
Example 1

5. Ch 4.3 Classwork #1 A. In the figure, a || b and m18 = 42. Find m22.
Transversals & Corresponding Angles
Classwork #1
A. In the figure, a || b and m18 = 42. Find m22.
A. 42
B. 84
C. 48
D. 138
Example 1a

6. Ch 4.3 Classwork #1 B. In the figure, a || b and m18 = 42. Find m25.
Transversals & Corresponding Angles
Classwork #1
B. In the figure, a || b and m18 = 42. Find m25.
A. 42
B. 84
C. 48
D. 138
Example 1b

7. Ch 4.3
Transversals & Corresponding Angles
4-1
4-2
4-3
Concept

8. Ch 4.3
Transversals & Corresponding Angles
Concept

9. Ch 4.3
Transversals & Corresponding Angles
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 Alternate Interior Angles Theorem
m2 = m3 Definition of congruent angles
125 = m3 Substitution
Answer: m3 = 125
Example 2

10. Ch 4.3
Transversals & Corresponding Angles
Classwork #2
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
Example 2

11. Ch 4.3 A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
Transversals & Corresponding Angles
Find Values of Variables
A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
5  7 Corresponding Angles Postulate
m5 = m7 Definition of congruent angles
2x – 10 = x Substitution
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer: x = 25
Example 3

12. Ch 4.3 B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
Transversals & Corresponding Angles
Find Values of Variables
B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
8  6 Corresponding Angles Postulate
m8 = m6 Definition of congruent angles
4y = m6 Substitution
m6 + m4 = 180 Supplement Theorem
4y + 4(y – 25) = 180 Substitution
4y + 4y – 100 = 180 Distributive Property
8y = 280 Additive Inverse Property.
y = 35 Multiplicative Inverse Property.
Example 3

13. Ch 4.3
Transversals & Corresponding Angles
Classwork #3
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
Example 3

14. Ch 4.3
Transversals & Corresponding Angles
Classwork #3
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
Example 3

15. Ch 4.3
Transversals & Corresponding Angles
Theorem 4-4
Concept