Proving Lines Parallel

1. Proving Lines Parallel

2. Check Skills You’ll Need Solve each equation. • 2x + 5 = 27 • 8a – 12 = 20 • x – 30 + 4x + 80 = 180 • 9x – 7 = 3 x + 29 Write down the converse of each conditional statement. Determine the truth value of the converse. 5. If a triangle is a right triangle, then it has a 90 degree angle. 6. If two angles are vertical angels, then they are congruent. 7. If two angles are same-side interior angles, then they are supplementary.

3. Postulate 3-2 If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. l 1 m 2

4. Theorem 3 – 3 Converse of the Alternate Interior Angles Theorem If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. If /_ 1 = /_ 2, then l llm l 1 4 m 2

5. Theorem 3 – 4 If two lines and a transversal for same-side interior angles that are supplementary, then two lines are parallel. If /_ 2 and /_ 4 are supplementary, then l llm l 1 4 m 2

6. Proving Theorem 3-3 Given /_ 1 = /_ 2 Prove: l ||m /_ 1 = /_ 2 Given /_ 1 = /_ 3 Vertical Angles /_ 2 = /_ 3 Transitive Property l ||m Postulate 3-2 l 3 1 m 2

7. Which lines, if any, must be parallel if ? Justify your answer with a theorem or postulate. 3 E C 4 D 1 K 2 DE || KC by theorem 3-3, the converse of the alternate interior angles theorem: If alternate interior angles are congruent, then the lines are parallel.

8. Theorem 3-5 If two lines are parallel to the same line, then they are parallel to each other Theorem 3-6 In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. a b c t m n

9. Given: r t, s t Prove: r||t m/_ 1 = 90; m/_ 2 = 90 m/_ 1 = m/_ 2 r||t r s 1 2 t

10. Find the value of x for which lllm 40 l m (2x + 6)