Question

Prove the consecutive interior angles theorem for two parallel lines, p and q, cut by a transversal, t. On the right side of the transversal, below the first parallel line, the angle is labeled 1. On the left side of the transversal, above the second parallel line, the angle is labeled 3. On the right side of the transversal, above the second parallel line, the angle is labeled 2. What is the relationship between angles 1, 2, and 3?

1) Angles 1 and 2 are supplementary, and angles 2 and 3 are supplementary.
2) Angles 1 and 2 are congruent, and angles 2 and 3 are congruent.
3) Angles 1 and 3 are supplementary, and angles 2 and 3 are congruent.
4) Angles 1 and 2 are congruent, and angles 1 and 3 are congruent.

Answer 1

The consecutive interior angles theorem states that when two parallel lines, p and q, are cut by a transversal, t, the angles on the same side of the transversal and between the parallel lines are congruent.

Step-by-step explanation:

The consecutive interior angles theorem states that when two parallel lines, p and q, are cut by a transversal, t, the angles on the same side of the transversal and between the parallel lines are congruent.

In the given scenario, angles 1 and 2 are on the same side of the transversal and between the parallel lines, so according to the consecutive interior angles theorem, angles 1 and 2 must be congruent. Similarly, angles 2 and 3 are also on the same side of the transversal and between the parallel lines, so angles 2 and 3 must also be congruent.

Therefore, the correct relationship between angles 1, 2, and 3 is that angles 1 and 2 are congruent, and angles 2 and 3 are congruent. Option 2 is the correct answer.