Question

lines c and d are parallel lines cut by transversal p. which must be true by the corresponding angles theorem?
∠1 ≅ ∠7
∠3 ≅ ∠5
∠2 ≅ ∠6
∠5 ≅ ∠7

Explanation:

Step1: Recall corresponding angles theorem

When two parallel lines are cut by a transversal, corresponding angles are congruent.

Step2: Analyze each option

• For $\angle1\cong\angle7$: These are not corresponding angles.
• For $\angle3\cong\angle5$: These are alternate - interior angles.
• For $\angle2\cong\angle6$: $\angle2$ and $\angle6$ are in the same relative position (top - right) with respect to the parallel lines \(c\) and \(d\) and the transversal \(p\), so by the corresponding angles theorem, they are congruent.
• For $\angle5\cong\angle7$: These are vertical angles.

Answer:

\(\angle2\cong\angle6\)