Parallel Lines and Angles

Chapter 3

Standardized Test Prep answers

1. B2. G3. A4. G5. C6. H7. A8. G9. C10. I11. C12. D13. B14. B15. B16. 6.3217. 45

18.a. (6, 2) b. 10

19.

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

10. a. def. perp. linesb. Def. of rt. <c. Corr <‘s are congruentd. Subst.e. Def. of rt. <f. Def of perp. Lines

11. 75, 105 corr, ssi12. 120, 60 corr, ssi13. 100, 70 ssi, alt. int.14. 70, 70, 11015. 25, 65, 6516. 20, 100, 8017. 52, 12818. One angle19. 2

20. 421. 222. 423. 3224. X = 76, y = 37, v = 42, w = 2525. X = 135, y = 4526. Discuss27. Trans means across28. Discuss29.Alt. int. are congruent30.57, ssi31.Same-side ext. are

supp….discuss32. m<1= m<2 v.a. congruent33.Never34.Sometimes35.Sometimes36.sometimes

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 polygonEquilateral and equiangular

Interior Angle Sum(n-2)*180

Exterior Angle Sum360

Constructing an arch

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!

 

                

              

 

                

              

              

                 

 

                

              

 

                

              

 

              

                

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

3. 65 corr; 65 V.A4. 85 AI; 110 SSI5. 85 corr; 95 SSI6. 70 corr; 110 SSI7. Yes8. Yes9. No10. No11. 512. 2513. 614. 7519. given, corr <‘s are congruent, given, transitive property, converse of

corresponding <‘s postulate21. Discuss22. 10923. 85, 100, 10028. 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 Review www.phsuccessnet.com

Test Review practice problems/proofshandout

Work on Polygon Arch projectdesignbuild 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.