Lesson 3-2

Angles and Parallel Lines

5-Minute Check on Lesson 3-15-Minute Check on Lesson 3-15-Minute Check on Lesson 3-15-Minute Check on Lesson 3-1 Transparency 3-2

Refer to the figure.

1. Name all planes parallel to MNR.

2. Name all segments skew to MP.

Give the special name for each angle pair in the figure.

3. 1 and 5

4. 3 and 8

5. 4 and 6

6. How many pairs of alternate interior angles are there in the figure above?Standardized Test Practice:

A CB D1 2 3 4

5-Minute Check on Lesson 3-15-Minute Check on Lesson 3-15-Minute Check on Lesson 3-15-Minute Check on Lesson 3-1 Transparency 3-2

Refer to the figure.

1. Name all planes parallel to MNR. Plane POS (can benamed with any 3 letters from POST)

2. Name all segments skew to MP. TS, QR, NR, OS

Give the special name for each angle pair in the figure.

3. 1 and 5 corresponding angles

4. 3 and 8 consecutive interior angles

5. 4 and 6 alternate exterior angles

6. How many pairs of alternate interior angles are there in the figure above?Standardized Test Practice:

A CB D1 2 3 4

Objectives

• Use the properties of parallel lines to determine congruent angles

• Use algebra to find angle measures

Vocabulary

• No new vocabulary words or symbols

Parallel Lines and Transversals

Postulate/ Theorem

StatementIf two parallel lines are cut by a transversal,

Examples

Corresponding Angles Post.

then each pair of corresponding angles is congruent

1 5, 2 6, 3 7, 4 8

Alternate Interior Angles Thrm

then each pair of alternate interior angles is congruent

3 6, 4 5

Consecutive Interior Angles Thrm

then each pair of consecutive interior angles is supplementary

m3 + m5 = 180°, m4 + m6 = 180°

Alternate Exterior Angles Thrm

then each pair of alternate exterior angles is congruent

1 8, 2 7

Perpendicular Transversal Thrm

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

None illustrated

t

k

l

1 23 4

5 67 8

Answer:

Corresponding Angles Postulate

Vertical Angles Theorem

Transitive Property

Definition of congruent angles

Substitution

In the figure x || y andm11 = 51. Find m16.

Answer: m19 = 138, and m25 = 42

In the figure, a || b and m18 = 42. Find m19 and m 25

What is the measure of RTV?

You need to find RTV. Be sure to identify it correctly on the figure. Look for patterns!!

Solve the Test Item

Alternate Interior Angles Theorem

Definition of congruent angles

Substitution

Definition of congruent angles

Alternate Interior Angles Theorem

Angle Addition Postulate

Substitution

What is the measure of IGE? Answer: 93

IfALGEBRA and

find x and y.

Find x.

by the Corresponding Angles Postulate.

Definition of congruent angles

Substitution

Subtract x from each side and add 10 to each side.

Definition of congruent angles

Substitution

Find y.

by the Alternate Exterior Angles Theorem.

Simplify.

Add 100 to each side.

Divide each side by 4.

Answer:

Substitution

Answer: x = 12 and y = 20

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

Decision Tree for Special Pairs

Where are the two angles?

Are they onopposite sides of transversal

Are they onopposite sides of transversal

Are they onopposite sides of transversal

None

Alt Exterior

Consecutive Int

Alt Interiorbo

thin

teri

or

one ofeach

both

exterior

yes

yes

Corresponding

None

yes

no

no

no

Answer: many combinations are possible

Identification: Determine what each of these angle pairs are in the drawing below:

5

4

1113 14 8

9

6 1216 15

10

7

Acute Angle:

Alternate Interior Angles:

Alternate Exterior Angles:

Corresponding Angles:

Consecutive Interior Angles:

Linear Pair of Angles:

Obtuse Angle:

Right Angle:

Vertical Angle Pair:

Answer: m1 = 130° m4 = 50°.

ALGEBRA: If m4 = 2x + 16 and m4 = 2(4x – 3), find m1, and m4.

4

Answer: m1 = 114°, m2 = 114°, m3 = 114°, and m4 = 66°.

ALGEBRA: If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find m1, m2, m3, and m4.

4

Summary & Homework

• Summary:– Pairs of congruent angles formed by parallel lines

and a transversal are corresponding angles, alternate interior angles and alternate exterior angles

– Pairs of consecutive interior angles are supplementary

• Homework: – Day 1: pg 136 – 137: 1, 5-11, 14-19– Day 2: pg 136 – 137: 20-25, 26, 27, 29, 31, 39