Question

use the given information to prove that ∠8≅∠1. given: x || y prove: ∠8 = ∠1

Explanation:

Step1: Identify corresponding angles

Since \(x\parallel y\), \(\angle8\) and \(\angle4\) are corresponding angles, so \(\angle8=\angle4\) (Corresponding - angles postulate when two parallel lines are cut by a transversal).

Step2: Identify vertical - angles

\(\angle4\) and \(\angle1\) are vertical angles. Vertical angles are congruent, so \(\angle4 = \angle1\).

Step3: Use transitive property

By the transitive property of equality, if \(\angle8=\angle4\) and \(\angle4=\angle1\), then \(\angle8=\angle1\).

Answer:

\(\angle8\cong\angle1\) is proven using corresponding - angles postulate and vertical - angles congruence along with the transitive property.