3.3 Proofs with Parallel Lines

​3.3 Proofs with Parallel Lines

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"Never regard study as a duty but as the enviable opportunity to learn."

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​-Albert Einstein

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Multiple Choice

Which condition will prove that line l is parallel to line m? #10

• ∠1 ≅ ∠3

• ∠3 ≅ ∠5

• ∠1 ≅ ∠6

• ∠6 ≅ ∠5

Multiple Choice

Which could be used to prove the lines are parallel? #15

• Converse of the Alternate Interior AnglesTheorem

• Converse of the Same-Side (Consecutive Interior) Angles Postulate

• Converse of the Corresponding Angles Theorem

• Cannot be proved parallel

Multiple Choice

Why are the two lines parallel or not parallel? #19

• Converse of the Corresponding Angles Theorem

• Converse of the Alternate Interior Angles Theorem

• Converse of the Alternate Exterior Angles Theorem

• Converse of the Consecutive Interior(Same-Side Interior) Angles Theorem

• Not Enough Information to Prove Parallel

Multiple Choice

Which of the following is the reason the two lines are parallel? #21

• The Converse of the Corresponding Angles Theorem

• The converse of the Alternate Interior Angles Theorem

• The converse of the Alternate Exterior Angles Theorem

• The Converse of Consecutive Interior (Same-Side Interior) Angles Theorem

• Not Enough Information to Prove Parallel

Multiple Choice

Solve for x. #25

• A

• B

• C

• D

Multiple Choice

Find the measure of the angle indicated in bold. #28

• A

• B

• C

• D

Fill in the Blanks

What value of x proves that line p is parallel to line r? #8

HINT (SET EXPRESSIONS EQUAL TO EACH OTHER BECAUSE OF THE CONVERSE OF THE ALTERNATE EXTERIOR ANGLE THEOREM. THEN SOLVE FOR X.)

Multiple Choice

Find the measure of the angle indicated in bold. #27

• A

• B

• C

• D

Multiple Choice

What value of x would make the lines parallel? #36

• 13

• 35

• 37

• 78

• 102

Multiple Choice

If ∠5 ≌∠7, which of the following can be concluded? #33

• r is parallel to s by converse of Alternate Interior Angles Thm.

• u is parallel to v by Converse of Corresponding Angles Thm

• s is ⊥ u by Converse of Alternate Interior Angles Thm

• v ⊥ r by Converse of Alternate Exterior Angles Thm

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Multiple Choice

When constructing a line parallel to a given line, you will be... #2

• copying a segment

• bisecting a segment

• copying an angle

• constructing a perpendicular

Multiple Choice

In the image, line RS is _______ to line JQ. #3

HINT: CORRESPONDING ANGLES PROVE WHAT?

• parallel

• congruent

• similar

• perpendicular

Multiple Choice

Marsha is using a straightedge and compass to do the construction shown. Which best describes the construction Marsha is doing? #1

• a line through P parallel to line l

• a line through P intersecting line l

• a line through P congruent to line l

• a line through P perpendicular to line l

Multiple Choice

The students in Mr. Beal’s class were asked to construct a line parallel to line MN through point O. Four different student responses. Which student appears to have done the construction correctly? #6