Question

e the given information to prove that ∠7 ≅ ∠5. given: x || y prove: ∠7 ≅ ∠5

Explanation:

Step1: State the given information

Given \(x\parallel y\).

Step2: Use the property of alternate interior angles

When two parallel lines \(x\) and \(y\) are cut by a transversal, \(\angle7\) and \(\angle5\) are alternate interior angles. By the Alternate - Interior Angles Theorem, if two parallel lines are cut by a transversal, then alternate interior angles are congruent.

Answer:

\(\angle7\cong\angle5\) (by the Alternate - Interior Angles Theorem since \(x\parallel y\))