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 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: Recall parallel - line properties

When two parallel lines \(a\) and \(b\) are cut by a transversal \(c\), corresponding angles are congruent. Angles 2 and 5 are corresponding angles. So, \(\angle2\cong\angle5\) because corresponding angles formed by parallel lines cut by a transversal are congruent.

Step2: Recall vertical - angle properties

Angles 5 and 7 are vertical angles. Vertical angles are always congruent. So, \(\angle5\cong\angle7\) because vertical angles are congruent.

Step3: Use the transitive property of congruence

Since \(\angle2\cong\angle5\) and \(\angle5\cong\angle7\), by the transitive property of congruence (if \(A = B\) and \(B = C\), then \(A = C\) for angles, \(\angle2\cong\angle7\)).

Answer:

Angles 2 and 5 are congruent because they are corresponding angles formed by parallel lines cut by a transversal. Angles 5 and 7 are congruent because they are vertical angles. Then, \(\angle2\cong\angle7\) by the transitive property of congruence.