Question

choose all of the following statements that prove that e and f are parallel. m∠3 + m∠5 = 90° ∠6 ≅ ∠7 ∠1 ≅ ∠2 ∠4 ≅ ∠8 ∠1 ≅ ∠4

Explanation:

Step1: Recall parallel - line angle relationships

When two lines are parallel and cut by a transversal, corresponding angles are congruent, alternate - interior angles are congruent, and alternate - exterior angles are congruent.

Step2: Analyze each statement

• For \(m\angle3 + m\angle5=90^{\circ}\), this does not prove parallel lines. There is no parallel - line theorem related to the sum of \(\angle3\) and \(\angle5\) being \(90^{\circ}\).
• \(\angle6\cong\angle7\) are vertical angles, and vertical - angle congruence has nothing to do with proving lines parallel.
• \(\angle1\cong\angle2\) are adjacent angles formed by a straight line, and their congruence does not prove parallel lines.
• \(\angle1\cong\angle4\) are vertical angles, and vertical - angle congruence does not prove parallel lines.
• \(\angle4\cong\angle8\): \(\angle4\) and \(\angle8\) are corresponding angles. If corresponding angles are congruent when two lines are cut by a transversal, then the two lines are parallel.

Answer:

\(\angle4\cong\angle8\)