Vertical Angles Theorem

Theorem: Vertical angles are always congruent.

In the figure, 1 3 and 2 4.

Proof:

1 and 2 form a linear pair, so by the Supplement Postulate, they are supplementary. That is,

m1 + m2 = 180°.

2 and 3 form a linear pair also, so

m2 + m3 = 180°.

Subtracting m2 from both sides of both equations, we get

m1 = 180° − m2 = m3.

Therefore,

1 3.

You can use a similar argument to prove that 2 4.