Angles and Parallel Lines

LESSON 3–2

Five-Minute Check (over Lesson 3–1)

TEKS

Then/Now

Postulate 3.1: Corresponding Angles Postulate

Example 1: Use Corresponding Angles Postulate

Theorems: Parallel Lines and Angle Pairs

Proof: Alternate Interior Angles Theorem

Example 2: Real-World Example: Use Theorems about Parallel Lines

Example 3: Find Values of Variables

Theorem 3.4: Perpendicular Transversal Theorem

Over Lesson 3–1

A. RST

B. PON

C. STQ

D. POS

Choose the plane parallel to plane MNR.

Over Lesson 3–1

A. PM

B. TS

C. PO

D. MQ___

___

___

___

Choose the segment skew to MP.

Over Lesson 3–1

A. corresponding angles

B. vertical angles

C. consecutive interior angles

D. alternate exterior angles

Classify the relationship between 1 and 5.

Over Lesson 3–1

A. alternate interior angles

B. alternate exterior angles

C. corresponding angles

D. consecutive interior angles

Classify the relationship between 3 and 8.

Over Lesson 3–1

A. alternate interior angles

B. alternate exterior angles

C. corresponding angles

D. vertical angles

Classify the relationship between 4 and 6.

Over Lesson 3–1

A. OS

B. TS

C. NR

D. MQ

Which of the following segmentsis not parallel to PT?

Targeted TEKSG.6(A) Verify theorems about angles formed by theintersection of lines and line segments, includingvertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems.

Mathematical ProcessesG.1(A), G.1(G)

You named angle pairs formed by parallel lines and transversals.

• Use theorems to determine the relationships between specific pairs of angles.

• Use algebra to find angle measurements.

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

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

A. 42

B. 84

C. 48

D. 138

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

A. 42

B. 84

C. 48

D. 138

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

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

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.

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

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

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

Find Values of Variables

8 6 Corresponding AnglesPostulate

m8 = m6 Definition of congruentangles

4y = m6 Substitution

Find Values of Variables

m6 + m4 = 180 Supplement Theorem

4y + 4(y – 25) = 180 Substitution

4y + 4y – 100 = 180 Distributive Property

8y = 280 Add 100 to each side.

y = 35 Divide each side by 8.

Answer: y = 35

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

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

Angles and Parallel Lines

LESSON 3–2