Question

When two lines intersect, four angles are formed. It is not hard to believe that the nonadjacent angles in this arrangement are congruent. If you had to prove this to a skeptic, what reasons would you offer?

Answer 1

The reason I would offer is that: The congruent angles are vertical angles.

Vertical angles are pairs of opposite angles formed by intersecting lines.

They have equal measures, meaning the angles are congruent.

In geometric terms, if two lines intersect, the angles opposite each other are vertical angles.

Since the two lines intersect , then their will be 2 pairs of congruent angles. This is because vertical opposite angles are congruent or equal.

The non adjascent angles are vertical angles and they are equal.