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Properties of Parallel Lines

Properties of Parallel Lines. 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…. t. Transversal. 5. 6. 1. 3. l. 4. 2. m. 8. 7.

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Properties of Parallel Lines

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  1. Properties of Parallel Lines

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

  3. Properties of Parallel Lines The pairs of angles formed have special names… t Transversal 5 6 1 3 l 4 2 m 8 7

  4. Alternate Interior Angles <1 and <2 <3 and <4 t 5 6 1 3 l 4 2 m 8 7

  5. Same-side Interior Angles <1 and <4 <2 and <3 t 5 6 1 3 l 4 2 m 8 7

  6. Corresponding Angles <1 and <7 <2 and <6 <3 and <8 <4 and <5 t 5 6 1 3 l 4 2 m 8 7

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

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

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

  10. Two-Column Proof t Given: a|| b Prove: m<1 = m<3 Statements Reasons 4 a 3 1 b 1. 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 *

  11. Two-Column Proof t Given: a|| b Prove: <1 and <2 are supplementary Statements Reasons 3 a 2 1 b 1. a|| b 1. Given 2. 2. Corr. Angle Postulate 3. 3. Consecutive Angles

  12. Finding Angle Measures c d <1 <2 <3 <4 <5 <6 <7 <8 a || b c || d a 8 7 6 50° 2 5 4 b 1 3

  13. Using Algebra to Find Angle Measures Find the value of x and y. x = y = ▲ ▲ 50° y 70° x ▲ 2x y (y – 50) ▲

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