Parallel and Perpendicular Lines

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Presentation transcript:

Parallel and Perpendicular Lines Chapter 3 Parallel and Perpendicular Lines

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.

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

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

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

4 Pairs of Vertical Angles Are Congruent 1  4 2  3 1  4 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)

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

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 m4 + m2 = 180 m2 = m6 m4 + m6 = 180 4 & 6 are Supplementary

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

Use what you have learned! 2. Solve for angles a, b, c if l//m 1. Find m2 if l//m. m c a b 42 l 1 2 65 40 m l ma = 65 (Alt. Inter. ) mc = 40 (Alt. Inter. ) ma + mb + mc = 180 65 + mb + 40 = 180 m = 75 m1 = 42 (Corrsp. ) m1 + m2 = 180 42 + m2 = 180 m2 = 138

Solve for x and find the measure of each angle if l//m. x + x +40 = 180 2x + 40 = 180 -40 -40 2x = 140 x = 70

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