# 3-3 Parallel Lines and Transversals Holt Geometry Warm Up Warm Up Lesson Presentation Lesson...

date post

21-Jan-2016Category

## Documents

view

212download

0

Embed Size (px)

### Transcript of 3-3 Parallel Lines and Transversals Holt Geometry Warm Up Warm Up Lesson Presentation Lesson...

3-3Parallel Lines and TransversalsHolt GeometryWarm UpLesson PresentationLesson Quiz

Warm UpIdentify each angle pair.

1. 1 and 32. 3 and 63. 4 and 54. 6 and 7same-side int scorr. salt. int. s alt. ext. s3.3 Parallel Lines and Transversals

Prove and use theorems about the angles formed by parallel lines and a transversal.Objective3.3 Parallel Lines and Transversals

3.3 Parallel Lines and Transversals

Find each angle measure.Example 1: Using the Corresponding Angles PostulateA. mECFx = 70B. mDCEmECF = 70Corr. s Post.5x = 4x + 22Corr. s Post.x = 22Subtract 4x from both sides.mDCE = 5x= 5(22)Substitute 22 for x.= 1103.3 Parallel Lines and Transversals

Check It Out! Example 1 Find mQRS.mQRS = 180 x x = 118mQRS + x = 180Corr. s Post.= 180 118 = 62 Subtract x from both sides.Substitute 118 for x.Def. of Linear Pair3.3 Parallel Lines and Transversals

3.3 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.3.3 Parallel Lines and Transversals

Find each angle measure.Example 2: Finding Angle MeasuresA. mEDGB. mBDGmEDG = 75Alt. Ext. s Thm.mBDG = 105x 30 = 75Alt. Ext. s Thm.x = 105Add 30 to both sides.3.3 Parallel Lines and Transversals

Check It Out! Example 2 Find mABD.mABD = 2(25) + 10 = 602x + 10 = 3x 15Alt. Int. s Thm.Subtract 2x and add 15 to both sides.x = 25Substitute 25 for x.3.3 Parallel Lines and Transversals

Find x and y in the diagram.Example 3: Music ApplicationBy the Alternate Interior AnglesTheorem, (5x + 4y) = 55.By the Corresponding Angles Postulate, (5x + 5y) = 60. 5x + 5y = 60(5x + 4y = 55) y = 55x + 5(5) = 60Subtract the first equation from the second equation.x = 7, y = 5Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x.3.3 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. 3.3 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 = 120Alt. Ext. s Thm.; m2 = 1203. m3 = (50x + 20), m4= (100x 80)

4. m3 = (45x + 30), m5 = (25x + 10)Alt. Int. s Thm.; m3 = 120, m4 =120Same-Side Int. s Thm.; m3 = 120, m5 =603.3 Parallel Lines and Transversals

*

*View more*