Question

problem 3: (first taught in lesson 26) complete this sentence with the best of the choices given. if two lines form congruent alternate interior angles with a transversal, then the lines ______. after you pick your answer press go. a b c d e are perpendicular go

Explanation:

To solve this, we recall the Alternate Interior Angles Theorem (or its converse). The converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.

Let's analyze the options (even though only one option's text is partially shown here, based on the theorem):

• The key concept here is the relationship between alternate interior angles and the parallelism of lines. When alternate interior angles are congruent, the lines are parallel (not perpendicular, unless specific angle measures like 90° are involved, which isn't stated here).

Assuming the full set of options includes "are parallel" (since the given option "are perpendicular" is incorrect for this theorem), the correct answer would be based on the Alternate Interior Angles Converse. But since the user's image shows option A's text as "are perpendicular" (which is incorrect), and we need to apply the theorem:

The correct completion is that the lines "are parallel" (assuming that's one of the options, likely among B, C, D, E if A is "are perpendicular"). But based on the theorem:

If two lines form congruent alternate interior angles with a transversal, then the lines are parallel.

(Note: Since the user's image might have the full options, but based on the theorem, the correct answer is that the lines are parallel. If we assume the options include that, the answer would be the option with "are parallel".)

But since the user's current display shows option A as "are perpendicular" (incorrect), the correct answer (based on the theorem) is that the lines are parallel. So if we had to choose from the options (assuming one of B - E is "are parallel"), that's the correct one.

However, to answer based on the theorem:

The Alternate Interior Angles Converse: If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

So the correct completion is "are parallel".

Answer:

To solve this, we recall the Alternate Interior Angles Theorem (or its converse). The converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.

Let's analyze the options (even though only one option's text is partially shown here, based on the theorem):

• The key concept here is the relationship between alternate interior angles and the parallelism of lines. When alternate interior angles are congruent, the lines are parallel (not perpendicular, unless specific angle measures like 90° are involved, which isn't stated here).

Assuming the full set of options includes "are parallel" (since the given option "are perpendicular" is incorrect for this theorem), the correct answer would be based on the Alternate Interior Angles Converse. But since the user's image shows option A's text as "are perpendicular" (which is incorrect), and we need to apply the theorem:

The correct completion is that the lines "are parallel" (assuming that's one of the options, likely among B, C, D, E if A is "are perpendicular"). But based on the theorem:

If two lines form congruent alternate interior angles with a transversal, then the lines are parallel.

(Note: Since the user's image might have the full options, but based on the theorem, the correct answer is that the lines are parallel. If we assume the options include that, the answer would be the option with "are parallel".)

But since the user's current display shows option A as "are perpendicular" (incorrect), the correct answer (based on the theorem) is that the lines are parallel. So if we had to choose from the options (assuming one of B - E is "are parallel"), that's the correct one.

However, to answer based on the theorem:

The Alternate Interior Angles Converse: If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

So the correct completion is "are parallel".