Question

Lines c and d are parallel lines cut by transversal p.

Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8.

Which must be true by the corresponding angles theorem?

∠1 ≅ ∠7
∠2 ≅ ∠6
∠3 ≅ ∠5
∠5 ≅ ∠7

Answer 1

Only ∠2 ≅ ∠6.

Reason: corresponding angles are in the same relative position at each intersection — here 2 and 6 are both the upper‑right angles. (∠5 ≅ ∠7 is true too, but by the vertical angles theorem, not the corresponding‑angles theorem.)