Question

Given ∠1≅∠7, which lines, if any, must be parallel based on the given information? Justify your conclusion.

Answer 1

C//d because b is a transversal going through the two lines. Since one and seven are congruent and are alternate exterior angles, the two lines must be congruent because of the conv. of alt. exterior angles theorem.

Answer 2

Answer: c∥d, Converse of the Alternate Exterior Angles Theorem

Step-by-step explanation:

We know that the alternate exterior angles are angles that are on opposite sides of the transversal and are on outside the two lines.

• The alternate exterior angles theorem says that if the two lines are parallel, then the alternate exterior angles are congruent to each other.
• The converse of alternate exterior angles theorem says that if alternate exterior angles are congruent to each other then  the two lines are parallel.

From the given figure it is given that ∠1≅∠7, Hence, by converse of alternate exterior theorem c∥d.