Which of the following statements are true?

Question

Select all that apply.



Responses

p ∥ q because ∠2 ≅ ∠3.
p ∥ q because ∠2 ≅ ∠3.

p ∥ q because ∠5 ≅ ∠7.
p ∥ q because ∠5 ≅ ∠7.

r ∥ s because ∠2 ≅ ∠4.
r ∥ s because ∠2 ≅ ∠4.

r ∥ s because ∠5 ≅ ∠6.
r ∥ s because ∠5 ≅ ∠6.
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Answer 1

In order to determine which statements are true regarding the parallel lines and corresponding angles, we need to rely on the properties of alternate interior angles, corresponding angles, and consecutive interior angles relative to parallel lines.

Here’s a quick recap of relevant angle relationships:

1. If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
2. If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
3. If two lines are cut by a transversal and the consecutive interior angles (same-side interior angles) are supplementary, then the lines are parallel.

Now we can analyze each statement:

1. p ∥ q because ∠2 ≅ ∠3.

   • If ∠2 and ∠3 are corresponding angles, then p and q are parallel. This statement could be true depending on the definitions of the angles.

2. p ∥ q because ∠5 ≅ ∠7.

   • If ∠5 and ∠7 are corresponding angles (or are alternate interior angles), then p and q are parallel. This statement could also be true.

3. r ∥ s because ∠2 ≅ ∠4.

   • If ∠2 and ∠4 are alternate interior angles, then r and s are parallel. This could be true.

4. r ∥ s because ∠5 ≅ ∠6.

   • If ∠5 and ∠6 are corresponding angles or alternate interior angles, then r and s are parallel. This could also be true.

Given the lack of specific diagrammatic context, we assume the angles referenced maintain the properties cited.

Conclusion:

All statements have a potential truth depending on angle relationships:

• p ∥ q because ∠2 ≅ ∠3 (could be true)
• p ∥ q because ∠5 ≅ ∠7 (could be true)
• r ∥ s because ∠2 ≅ ∠4 (could be true)
• r ∥ s because ∠5 ≅ ∠6 (could be true)

Select all that apply.