Question

lines c and d are parallel lines cut by transversal p. which must be true by the corresponding angles theorem? \\( \angle 5 \cong \angle 7 \\) \\( \angle 1 \cong \angle 7 \\) \\( \angle 3 \cong \angle 5 \\) \\( \angle 2 \cong \angle 6 \\)

Explanation:

Step1: Recall the corresponding angles theorem

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

Step2: Identify corresponding angles

Corresponding angles are in the same relative position. $\angle2$ and $\angle6$ are in the same relative position (upper - right position at their respective intersections of the transversal with the parallel lines).
$\angle5\cong\angle7$ is due to vertical angles theorem. $\angle1\cong\angle7$ is not a case of corresponding angles. $\angle3\cong\angle5$ is alternate interior angles theorem.

Answer:

$\angle2\cong\angle6$