Properties of Parallel Lines.  Transversal: line that intersects two coplanar lines at two distinct points Transversal.

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Presentation transcript:

Properties of Parallel Lines

 Transversal: line that intersects two coplanar lines at two distinct points Transversal

Properties of Parallel Lines The pairs of angles formed have special names… Transversal l m t

Alternate Interior Angles <1 and <2 <3 and < l m t

Same-side Interior Angles <1 and <4 <2 and < l m t

Corresponding Angles <1 and <7 <2 and <6 <3 and <8 <4 and < l m t

Properties of Parallel Lines Postulate 3-1Corresponding Angles Postulate If a transversal intersects two parallel lines, then corresponding angles are congruent t l m line l || line m 1 2 m<1 =m <2

Properties of Parallel Lines Theorem 3-1Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then alternate interior angles are congruent. t l m line l || line m 1 2 m<2 = m<3 3

Properties of Parallel Lines Theorem 3-2Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then same-side interior angles are supplementary. t l m line l || line m 1 2 m<1 + m<2 = 180 3

Two-Column Proof Given: a || b Prove: m<1 = m<3 StatementsReasons a b t a || b 1. Given 2.2. Corr. Angle Postulate 3.3. Vert. Angles 4.4. Set Statement 1 = Statement 2 * This proves why alternate interior angles are congruent *

Two-Column Proof Given: a || b Prove: <1 and <2 are supplementary StatementsReasons a b t a || b 1. Given 2.2. Corr. Angle Postulate 3.3. Consecutive Angles

Finding Angle Measures <1 <2 <3 <4 <5 <6 <7 <8 a b c d a || bc || d °

Using Algebra to Find Angle Measures Find the value of x and y. x = y = ▲ ▲ x 50° y70° 2xy (y – 50) ▲ ▲

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