Question

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 symmetric property definition of substitution transitive property corresponding angles postulate

Explanation:

Step1: Identify angle - type for ∠2 and ∠5

∠2 and ∠5 are alternate - interior angles. Alternate - interior angles formed by parallel lines cut by a transversal are congruent.

Step2: Identify angle - type for ∠5 and ∠7

∠5 and ∠7 are vertical angles. Vertical angles are always congruent.

Step3: Determine congruence of ∠2 and ∠7

Since ∠2≅∠5 and ∠5≅∠7, by the transitive property of congruence (if a = b and b = c, then a = c), ∠2≅∠7.

Answer:

For the first blank: alternate - interior; for the second blank: vertical; for the third blank: transitive property