Question

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

Explanation:

• Corresponding angles theorem: When two parallel lines are cut by a transversal, corresponding angles are equal.
• Let's analyze each option:
• For \(\angle1\) and \(\angle7\): They are not corresponding angles.
• For \(\angle2\) and \(\angle6\): \(\angle2\) and \(\angle6\) are in the same relative position (upper - right) with respect to the parallel lines \(c\) and \(d\) and the transversal \(p\). So, by the corresponding angles theorem, \(\angle2=\angle6\).
• For \(\angle3\) and \(\angle5\): They are alternate interior angles (not corresponding angles).
• For \(\angle5\) and \(\angle7\): They are vertical angles (not corresponding angles).

Answer:

\(\angle2 = \angle6\)