**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,

*m*1 + *m*2 = 180°.

2 and 3 form a linear pair also, so

*m*2 + *m*3 = 180°.

Subtracting *m*2 from both sides of both equations, we get

*m*1 = 180° −* m*2 = *m*3.

Therefore,

1 3.

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