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 by parallel lines cut by a transversal are congruent. angles 5 and 7 are congruent because. therefore, angles 2 and 7 are congruent based on the. symmetric property, definition of substitution, transitive property, corresponding angles postulate

Explanation:

Step1: Recall angle - congruence rules

Since lines \(a\) and \(b\) are parallel and \(c\) is a transversal, angles 2 and 5 are corresponding angles. By the corresponding - angles postulate, corresponding angles formed by parallel lines and a transversal are congruent.

Step2: Analyze the relationship between angles 5 and 7

Angles 5 and 7 are vertical angles. By the definition of vertical angles, vertical angles are congruent.

Step3: Use the transitive property

We know that \(\angle2\cong\angle5\) (corresponding angles) and \(\angle5\cong\angle7\) (vertical angles). By the transitive property of congruence, if \(\angle2\cong\angle5\) and \(\angle5\cong\angle7\), then \(\angle2\cong\angle7\).

Answer:

The first blank should be filled with "corresponding angles postulate" and the second blank should be filled with "vertical angles are congruent" and the third blank should be filled with "transitive property".