Ch 4.3Transversals and

Corresponding Angles

Ch 4.3

Standard 7.0Students prove and use theorems involving the properties of parallel lines cut by a transversal.

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

Transversals & Corresponding Angles

Ch 4.3 Transversals & Corresponding Angles

Postulate 4-1

Use Corresponding Angles Postulate

A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.

Answer: m15 = 51

15 11 Corresponding Angles Postulate

m15 = m11 Definition of congruent angles

m15 = 51 Substitution

Ch 4.3 Transversals & Corresponding Angles

Use Corresponding Angles Postulate

B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.

Answer: m16 = 51

16 15 Vertical Angles Theorem

15 11 Corresponding AnglesPostulate

16 11 Transitive Property ()

m16 = m11 Definition of congruent angles

m16 = 51 Substitution

Ch 4.3 Transversals & Corresponding Angles

A. 42

B. 84

C. 48

D. 138

A. In the figure, a || b and m18 = 42. Find m22.

Ch 4.3 Transversals & Corresponding Angles

Classwork #1

A. 42

B. 84

C. 48

D. 138

B. In the figure, a || b and m18 = 42. Find m25.

Ch 4.3 Transversals & Corresponding Angles

Classwork #1

Ch 4.3

4-1

4-2

4-3

Transversals & Corresponding Angles

Ch 4.3 Transversals & Corresponding Angles

Use Theorems about Parallel Lines

FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.

2 3 Alternate Interior Angles Theorem

m2 = m3 Definition of congruent angles

125 = m3 Substitution

Answer: m3 = 125

Ch 4.3 Transversals & Corresponding Angles

A. 25

B. 55

C. 70

D. 125

FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.

Ch 4.3 Transversals & Corresponding Angles

Classwork #2

A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.

Find Values of Variables

5 7 Corresponding Angles Postulate

m5 = m7 Definition of congruent angles

2x – 10 = x + 15 Substitution

x – 10 = 15 Subtract x from each side.

x = 25 Add 10 to each side.

Answer: x = 25

Ch 4.3 Transversals & Corresponding Angles

B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.

Find Values of Variables

8 6 Corresponding Angles Postulate

m8 = m6 Definition of congruent angles

4y = m6 Substitution

Ch 4.3 Transversals & Corresponding Angles

m6 + m4= 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.

A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.

A. x = 9

B. x = 12

C. x = 10

D. x = 14

Ch 4.3 Transversals & Corresponding Angles

Classwork #3

B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y.

A. y = 14

B. y = 20

C. y = 16

D. y = 24

Ch 4.3 Transversals & Corresponding Angles

Classwork #3

Ch 4.3 Transversals & Corresponding Angles

Theorem 4-4