Parallel Lines and Angles

1. Parallel Lines and Angles Chapter 3

2. Standardized Test Prep answers • B • G • A • G • C • H • A • G • C • I • C • D • B • B • B • 6.32 • 45 • a. (6, 2) b. 10

3. Proving Lines parallel • Corresponding Angles Postulate • If two lines are parallel then corresponding angles formed by them are congruent • Alternate Interior Angles Theorem • If two lines are parallel then alternate interior angles formed by them are congruent • Same-Side Interior Angles Theorem • If two lines are parallel then same-side interior angles formed by them are supplementary

4. Answers: 3-1 #10-36 • 20. 4 • 21. 2 • 22. 4 • 23. 32 • 24. X = 76, y = 37, v = 42, w = 25 • 25. X = 135, y = 45 • 26. Discuss • 27. Trans means across • 28. Discuss • Alt. int. are congruent • 57, ssi • Same-side ext. are supp….discuss • m<1= m<2 v.a. congruent • Never • Sometimes • Sometimes • sometimes 10. a. def. perp. lines • Def. of rt. < • Corr <‘s are congruent • Subst. • Def. of rt. < • Def of perp. Lines • 75, 105 corr, ssi • 120, 60 corr, ssi • 100, 70 ssi, alt. int. • 70, 70, 110 • 25, 65, 65 • 20, 100, 80 • 52, 128 • One angle • 2

5. Converses of the parallel lines conjectures • If corresponding angles are congruent then the lines must be parallel • If alternate interior angles are congruent then the lines must be parallel • If same side interior angles are supplementary then the lines must be parallel.

6. Starter: Parallel & Perpendicular lines • If two lines are parallel to the same line then they are parallel to eachother WRITE A PROOF • If two lines in a plane are perpendicular to the same line, then they are parallel to eachother. WRITE A PROOF

7. Think/Pair share: What is a polygon? List all characteristics you believe make something a polygon and anything you already know about polygons.

8. Polygons • Convex vs. non-convex (concave) Formulas work for convex polygons only • Regular polygon Equilateral and equiangular • Interior Angle Sum (n-2)*180 • Exterior Angle Sum 360

9. According to legend when the Romans made an arch, they would make the architect stand under it while the wooden support was removed. That was one way to be sure that architects carefully designed arches that wouldn't fall! Constructing an arch

10. Arch intro: Brainstorm • What shape do you think the blocks could be? • Look at the interior of the arch. Sketch it in 2-D. • How many blocks would we need if our class were to build an arch?

11. STARTER: Test Next Block 1. What can you conclude about the bisector of an exterior angle in a triangle if the remote interior angles are congruent? Write a proof to justify your response. 2. HW Peer edit (answers on next slide)

12. Chapter Test • 65 corr; 65 V.A • 85 AI; 110 SSI • 85 corr; 95 SSI • 70 corr; 110 SSI • Yes • Yes • No • No • 5 • 25 • 6 • 75 • given, corr <‘s are congruent, given, transitive property, converse of corresponding <‘s postulate • Discuss • 109 • 85, 100, 100 28. 30

13. MINLESSON REQUESTS SIGN UP FOR THE FOLLOWING: • Parallel lines & triangle sum theorem problems • Converse of parallel lines theorems & problems • Theorems, Postulates & Proofs • Polygon Angle Sums

14. TODAY • Scan Chapter Reviewwww.phsuccessnet.com • Test Review practice problems/proofs handout • Work on Polygon Arch project design build block Keep track of what you completed today on a blank sheet of paper. Anything not completed must be done for homework. Test & arch building next block.