Download presentation

Presentation is loading. Please wait.

1
**Parallel and Perpendicular Lines**

Chapter 3 Parallel and Perpendicular Lines

2
**Properties of Parallel Lines**

Sec. 3-1 Properties of Parallel Lines Objective: a) Identify Angles formed by Two Lines & a Transversal. b) To Prove & Use Properties of Parallel Lines.

3
**Parallel Lines – Two lines in the same plane which never intersect. **

Symbol: “ // ” Transversal – A line that intersects two // lines. 8 Special Angles are formed. t 1 2 Interior Portion of the // Lines m 3 4 5 6 n 7 8

4
**Corresponding Angles Most Important Angle Relationship**

Always Congruent Cut the Transversal & lay the top part onto the bottom part. Overlapping Angles are Corresponding. Corresponding Angles 1 & 5 2 & 6 3 & 7 4 & 8 1 2 3 4 5 6 7 8

5
**P(3 – 1) Corresponding Angle Postulate**

If a Transversal Intersects two // lines, then the corresponding angles are Congruent. 1 2 3 4 5 6 7 8

6
**4 Pairs of Vertical Angles Are Congruent 1 4 2 3 **

1 2 3 5 8 6 7 3 4 5 6 7 8 Special Interior Angles 3 & 6 4 & 5 Alternate Interior Angles Are congruent 3 & 5 4 & 6 Same-Sided Interior Angles Are Supplementary (= 180)

7
**Th (3-1) Alternate Interior Angle Theorem**

If a Transversal intersects two // lines, then the alternate interior angles are congruent. 1 2 l Given: l // m Prove: 3 6 3 4 5 6 m 7 8 Statements l // m 3 7 7 6 3 6 Reasons Given Corrsp. Angles are Congruent Def. of Vertical Angles Subs

8
**Th (3-2) Same-Sided Interior Angle Theorem**

If a Transversal intersects two // lines, then the same-sided interior angles are supplementary. 1 2 l 3 4 Given: l // m Prove: 4 & 6 are Supplementary 5 6 m 7 8 Reasons Given Add. Postulate Corrsp. s are Subs Def of Supplementary Statements l // m m4 + m2 = 180 m2 = m6 m4 + m6 = 180 4 & 6 are Supplementary

9
**Examples 1 & 2 Solve for the missing s Solve for x, then for each .**

14x – 5 = 13x -5 = -x 5 = x 5x – 20 +3x = 180 8x = 200 x = 25

10
**Use what you have learned!**

2. Solve for angles a, b, c if l//m 1. Find m2 if l//m. m c a b 42 l 1 2 65 40 m l ma = 65 (Alt. Inter. ) mc = 40 (Alt. Inter. ) ma + mb + mc = 180 65 + mb + 40 = 180 m = 75 m1 = 42 (Corrsp. ) m1 + m2 = 180 42 + m2 = 180 m2 = 138

11
**Solve for x and find the measure of each angle if l//m.**

x + x +40 = 180 2x + 40 = 180 2x = 140 x = 70

Similar presentations

Presentation is loading. Please wait....

OK

PARALLEL LINES and TRANSVERSALS.

PARALLEL LINES and TRANSVERSALS.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Marketing ppt on product Ppt on travels and tourism Ppt on tungsten inert gas welding Ppt on special types of chromosomes genes Ppt on transportation and excretion in human body Ppt on limitation act pakistan Ppt on mathematics for class 9 Ppt on group discussion topics Ppt on email etiquettes presentation boards Ppt on cross docking case