Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals3-2 Angles Formed by Parallel Lines and

Transversals

Holt Geometry

Bellwork1. Martha’s salary is $10 per hour. Doug’s salary is $8 per hour. Doug also gets $40 for expenses each week. Last week, Martha and Doug earned the same amount. How many hours did each work last week? A. 4 B. 5 C. 20 D. 40 2. You have a base salary of 150,000 plus 3% commission on sales. Sales were $125,000 this year. What was your total pay?  3. Between which two integers is the square root of 60? 5 and 6 6 and 7 7 and 8 8 and 9

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Warm UpIdentify each angle pair.

1. 1 and 3

2. 3 and 6

3. 4 and 5

4. 6 and 7 same-side int s

corr. s

alt. int. s

alt. ext. s

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Prove and use theorems about the angles formed by parallel lines and a transversal.

Objective

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Find each angle measure.

Example 1: Using the Corresponding Angles Postulate

A. mECF

x = 70

B. mDCE

mECF = 70°

Corr. s Post.

5x = 4x + 22 Corr. s Post.

x = 22 Subtract 4x from both sides.

mDCE = 5x

= 5(22) Substitute 22 for x.

= 110°

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Check It Out! Example 1

Find mQRS.

mQRS = 180° – x

x = 118

mQRS + x = 180°

Corr. s Post.

= 180° – 118°

= 62°

Subtract x from both sides.

Substitute 118° for x.

Def. of Linear Pair

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

If a transversal is perpendicular to two parallel lines, all eight angles are congruent.

Helpful Hint

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Remember that postulates are statements that are accepted without proof.

Since the Corresponding Angles Postulate is given as a postulate, it can be used to prove the next three theorems.

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Find each angle measure.

Example 2: Finding Angle Measures

A. mEDG

B. mBDG

mEDG = 75° Alt. Ext. s Thm.

mBDG = 105°

x – 30° = 75° Alt. Ext. s Thm.

x = 105 Add 30 to both sides.

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Check It Out! Example 2

Find mABD.

mABD = 2(25) + 10 = 60°

2x + 10° = 3x – 15° Alt. Int. s Thm.

Subtract 2x and add 15 to both sides.

x = 25

Substitute 25 for x.

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Find x and y in the diagram.

Example 3: Music Application

By the Alternate Interior AnglesTheorem, (5x + 4y)° = 55°.

By the Corresponding Angles Postulate, (5x + 5y)° = 60°.

5x + 5y = 60–(5x + 4y = 55) y = 5

5x + 5(5) = 60

Subtract the first equation from the second equation.

x = 7, y = 5

Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x.

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Check It Out! Example 3

Find the measures of the acute angles in the diagram.

An acute angle will be 180° – 125°, or 55°.

By the Alternate Exterior AnglesTheorem, (25x + 5y)° = 125°.

By the Corresponding Angles Postulate, (25x + 4y)° = 120°.

The other acute angle will be 180° – 120°, or 60°.

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Practice Time!p. 158 #7-27o, 31,34-36,37,39,43

Holt Geometry

3-2 Angles Formed by Parallel Lines and Transversals

Lesson QuizState the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures.

1. m1 = 120°, m2 = (60x)°

2. m2 = (75x – 30)°, m3 = (30x + 60)°

Corr. s Post.; m2 = 120°, m3 = 120°

Alt. Ext. s Thm.; m2 = 120°

3. m3 = (50x + 20)°, m4= (100x – 80)°

4. m3 = (45x + 30)°, m5 = (25x + 10)°Alt. Int. s Thm.; m3 = 120°, m4 =120°

Same-Side Int. s Thm.; m3 = 120°, m5 =60°