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Properties of Parallel Lines

Properties of Parallel Lines. Check Skills You’ll need. Solve each equation x + 2x + 3x = 180 (w+23)+(4w+7)=180 90=2y – 30 180 – 5y = 135 Write an equation and solve the problem 5. The sum of m /_ 1and twice its complement is 146.

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Properties of Parallel Lines

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  1. Properties of Parallel Lines

  2. Check Skills You’ll need Solve each equation • x + 2x + 3x = 180 • (w+23)+(4w+7)=180 • 90=2y – 30 • 180 – 5y = 135 Write an equation and solve the problem 5. The sum of m/_ 1and twice its complement is 146. 6. The measures of two supplementary angles are in the ratio 2:3. Find their measures.

  3. What is a transversal? A transversal is a line that intersects two coplanar lines at two distinct points. The diagram shows the eight angles formed by a transversal t and two lines l and m. t 5 6 l 1 3 m 4 2 7 8

  4. 1 3 alternate interior angles 4 2 1 same-side interior angles 3 4 2

  5. 5 6 1 3 4 2 7 8 corresponding angles

  6. Postulate 3-1 If a transversal intersects two parallel lines, then corresponding angles are congruent. 5 6 1 3 4 2 7 8

  7. Theorem 3 – 1 If a transversal intersects two parallel lines, then alternate interior angles are congruent. 1 3 4 2

  8. Theorem 3-2 If a transversal intersects two parallel lines, the same-side interior angles are supplementary 1 3 4 2

  9. Proving If a transversal intersects two parallel lines, then alternate interior angles are congruent. Given: a ||b Prove: /_ 1 = /_ 3 4 3 1 1. a|| b given 2. /_ 1 = /_ 4 Corresponding Angles Postulate 3. /_ 4 = /_ 3 Vertical angles 4. /_ 1 = /_ 3 Transitive property

  10. Proving If a transversal intersects two parallel lines, then alternate interior angles are congruent. Given: a ||b Prove: /_ 1 = /_ 2 are supplementary 3 2 1

  11. Find the measures of all the angles f a 3 e b 50 g h c d

  12. Find the values of x and y 50 70 x y

  13. Your most awaited part It’s TEST TIME

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