Proving Lines Parallel Answers

1

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Which theorem correctly justifies why the lines m and n are parallel when cut by transversal k?

A

converse of the corresponding angles theorem

B

converse of the alternate interior angles theorem

C

converse of the same side interior angles theorem

D

converse of the alternate exterior angles theorem

2

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Which diagram shows parallel lines cut by a transversal?

A

[Image: 2 lines are cut by a transversal. At the intersect...]

B

[Image: 2 lines are cut by a transversal. At the intersect...]

C

[Image: 2 lines are cut by a transversal. At the intersect...]

3

Letters x, y, and z are angle measures. Which equations would guarantee that lines p and q are parallel? Check all that apply.

A

x = z

B

x + y = 180°

C

x + z = 180°

D

x = y

E

z = 180°

4

Which lines are parallel? Justify your answer.

A

Lines p and q are parallel because same side interior angles are congruent.

B

Lines p and q are parallel because alternate exterior angles are congruent

C

Lines l and m are parallel because same side interior angles are supplementary

D

Lines l and m are parallel because alternate interior angles are supplementary.

5

Question text not available

Answer:

70

6

If angle 1 is 110°, what would the other angle measures have to be in order for m || n and q || p?

Answer:

110

7

Question text not available

Answer:

70

8

Find the values of x and y that make k || j and m || n.

Answer:

80

9

Question text not available

Answer:

130

10

Given: ∠T ≅ ∠V; ST || UVProve: TU || VW

Answers:

♣ = ♦ = ♠ =:alternate interior angles theorem

♣ = ♦ = ♠ =:transitive property

♣ = ♦ = ♠ =:converse alternate interior angles theorem

11

Complete the missing parts of the paragraph proof.

Answers:

We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to an:it is given

We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to an:angle 2

We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to an:angle 3

We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to an:converse alternate exterior angles theorem

12

angle 1 ✔ angle 2 line m

A

angle 1

B

✔ angle 2

C

line m

13

angle 1 angle 2 ✔ angle 3

A

angle 1

B

angle 2

C

✔ angle 3

14

corresponding angles theorem ✔ converse alternate exterior angles theorem converse same side interior angles theorem

A

corresponding angles theorem

B

✔ converse alternate exterior angles theorem

C

converse same side interior angles theorem

15

Given: ∠T ≅ ∠V; ST || UVProve: TU || VW

Answers:

♣ = ♦ = ♠ =:alternate interior angles theorem

♣ = ♦ = ♠ =:transitive property

♣ = ♦ = ♠ =:converse alternate interior angles theorem

16

givenlinear pair postulate✔ transitive property

A

given

B

linear pair postulate

C

✔ transitive property

17

✔ converse alternate interior angles theoremconverse corresponding angles theoremconverse alternate exterior angles theorem

A

✔ converse alternate interior angles theorem

B

converse corresponding angles theorem

C

converse alternate exterior angles theorem

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