Vertical Angles Theorem

Theorem: Vertical angles are always congruent.

In the figure, 13and24 .

Proof:

1and2 form a linear pair, so by the Supplement Postulate, they are supplementary. That is,

m1+m2=180° .

2and3 form a linear pair also, so

m2+m3=180° .

Subtracting m2 from both sides of both equations, we get

m1=180°m2=m3 .

Therefore,

13 .

You can use a similar argument to prove that 24 .