Question

If p is parallel to q, which pair of angles must be congruent?

Answer 1

Vertical angles are congruent whether the lines are parallel or not.
Corresponding angles are congruent.
Alternate interior and alternate exterior angles are congruent.
1 & 4, 2 & 3, 3 & 6, 4 & 5, 1 & 8, 2 & 7, 5 & 8, 6 & 7, 3 & 7, 1 & 5, 2 & 6, 4 & 8
I think I got all of them!

Answer 2

When two lines are parallel and are intersected by a third line,

Then the pairs of corresponding angles are congruent.

The pairs of Alternate interior angles are congruent.

More names can be given to these angles.

But when we consider all corresponding and alternate angles, all angles are covered.

In the given figure

<2 = <6, <4 = <8, <1 = <5 and <3= <7 are all corresponding angles.   ..(1)

Also < 4 = <5 & <3 = <6 are alternate interior angles.    ...(2)

If we compare Statement (1) & statement (2)

We get

<1 = <5 = <8 = <4

<3 = <7 = <6 = <2

So all red dotted angles are equal

Also all black dotted angles are equal.