Question

given: a and b are parallel and c is a transversal. prove: ∠2 ≅ ∠7
use the drop-down menus to complete the paragraph proof showing that alternate interior angles are congruent.
we know that lines a and b are parallel and that line c is a transversal because that is given. we can tell that angles 2 and 5 are congruent because
angles are congruent. angles 5 and 7 are congruent because
angles by parallel lines cut by a transversal are congruent. therefore, angles 2 and 7 are congruent based on the
.

Explanation:

Step1: Analyze ∠2 and ∠5

Angles 2 and 5 are vertical angles. Vertical angles are always congruent. So the first drop - down should be "vertical" as vertical angles are congruent.

Step2: Analyze ∠5 and ∠7

Since lines \(a\) and \(b\) are parallel and \(c\) is a transversal, ∠5 and ∠7 are alternate interior angles. Alternate interior angles formed by parallel lines cut by a transversal are congruent. So the second drop - down should be "alternate interior".

Step3: Analyze the relationship between ∠2, ∠5 and ∠7

We know that ∠2 ≅ ∠5 (vertical angles) and ∠5 ≅ ∠7 (alternate interior angles). By the transitive property of congruence, if ∠2 ≅ ∠5 and ∠5 ≅ ∠7, then ∠2 ≅ ∠7. So the third drop - down should be "transitive property of congruence".

Answer:

First drop - down: vertical; Second drop - down: alternate interior; Third drop - down: transitive property of congruence