Question

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

Explanation:

Step1: Recall the corresponding angles theorem

When two parallel lines are cut by a transversal, corresponding angles are congruent. Corresponding angles are in the same relative position.

Step2: Analyze each option

• For $\angle1$ and $\angle7$: They are not in corresponding positions.
• For $\angle2$ and $\angle6$: $\angle2$ and $\angle6$ are in the same relative position (upper - right position with respect to the parallel lines \(c\) and \(d\) and the transversal \(p\)). By the corresponding angles theorem, if \(c\parallel d\) and \(p\) is the transversal, then \(\angle2\cong\angle6\).
• For $\angle3$ and $\angle5$: They are alternate interior angles (not corresponding angles).
• For $\angle5$ and $\angle7$: They are vertical angles (not corresponding angles).

Answer:

\(\angle2\cong\angle6\) (i.e., the second option \(\angle2\cong\angle6\))