Question

Lines m and n are parallel lines cut by a transversal l.

Answer 1

Answer:

Angles 1 and 3 are congruent as vertical angles; angles 3 and 7 are congruent as corresponding angles.

Step-by-step explanation:

<1 and <3 are vertical angles  because they are formed by the same lines and are opposite each other .  3 and 7 are corresponding angles because they are in the same position at each intersection where a straight line crosses two others.  Since the lines are parallel, they are equal  That makes 1 and 7 equal

Answer 2

Answer:

B. Angles 1 and 3 are congruent as vertical angles; angles 3 and 7 are congruent as corresponding angles.

Step-by-step explanation:

We need statements that will link angle 1 and angle 7 together. Just from looking at the answer choices, we can already see that choice B is the only one that includes both 1 and 7, so that's a very possible correct answer.

Delving more deeply though, let's look at B. Angles 1 and 3 are called vertical angles and by definition, they're congruent. Also, angles 3 and 7 are called same-side angles, or corresponding angles, and again by definition, they're congruent. Thus, B gives correct reasoning to prove that since ∠1 = ∠3 and ∠3 = ∠7, then ∠1 = ∠7.

The answer is B.