Question

Which must be true according to the corresponding angles theorem?

1.∠1 is congruent to ∠7.
2.∠2 is congruent to ∠6.
3.∠3 is congruent to ∠5.
4.∠5 is congruent to ∠7.

Answer 1

According to the corresponding angles theorem, ∠1 is congruent to ∠7. Hence, 1) is correct.

Step-by-step explanation:

The corresponding angles theorem states that when two parallel lines are intersected by a transversal, the corresponding angles formed are congruent.

In the given options:

1. ∠1 and ∠7 are corresponding angles, so they must be congruent. Therefore, option 1 must be true.
2. ∠2 and ∠6 are alternate interior angles, not corresponding angles. Therefore, option 2 is not necessarily true.
3. ∠3 and ∠5 are alternate interior angles, not corresponding angles. Therefore, option 3 is not necessarily true.
4. ∠5 and ∠7 are alternate interior angles, not corresponding angles. Therefore, option 4 is not necessarily true.

Based on the corresponding angles theorem, the only true statement is option 1: ∠1 is congruent to ∠7.