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Parallel Lines and Angles. Chapter 3. 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. Proving Lines parallel. Corresponding Angles Postulate If two lines are parallel then corresponding angles formed by them are congruent

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## Parallel Lines and Angles

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**Parallel Lines and Angles**Chapter 3**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**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**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**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.**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**Think/Pair share:**What is a polygon? List all characteristics you believe make something a polygon and anything you already know about polygons.**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**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**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?**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)**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**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**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.

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