Yes, that's correct. According to the Alternate Interior Angles Theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are indeed parallel.

Here are the steps to understand this:

1. Two lines are cut by a transversal, creating several angles.
2. Identify the alternate interior angles. These are non-adjacent angles that lie on opposite sides of the transversal.
3. If these alternate interior angles are congruent (equal in measure), then according to the Alternate Interior Angles Theorem, the two lines cut by the transversal must be parallel.

This is because parallel lines cut by a transversal have congruent alternate interior angles, so if the alternate interior angles are congruent, it implies the lines must be parallel.

Question

Yes, that's correct. According to the Alternate Interior Angles Theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are indeed parallel.

Here are the steps to understand this:

1. Two lines are cut by a transversal, creating several angles.
2. Identify the alternate interior angles. These are non-adjacent angles that lie on opposite sides of the transversal.
3. If these alternate interior angles are congruent (equal in measure), then according to the Alternate Interior Angles Theorem, the two lines cut by the transversal must be parallel.

This is because parallel lines cut by a transversal have congruent alternate interior angles, so if the alternate interior angles are congruent, it implies the lines must be parallel.

Knowee AI · Accepted Answer

Yes, that's correct. According to the Alternate Interior Angles Theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are indeed parallel.

Here are the steps to understand this:

1. Two lines are cut by a transversal, creating several angles.
2. Identify the alternate interior angles. These are non-adjacent angles that lie on opposite sides of the transversal.
3. If these alternate interior angles are congruent (equal in measure), then according to the Alternate Interior Angles Theorem, the two lines cut by the transversal must be parallel.

This is because parallel lines cut by a transversal have congruent alternate interior angles, so if the alternate interior angles are congruent, it implies the lines must be parallel.

If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

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