Vertical angles are congruent is that an example of a theorem

Proof:

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

m∠1+m∠2=180° m∠1+m∠2=180°.

∠2and∠3 ∠2and∠3 form a linear pair also, so

m∠2+m∠3=180° m∠2+m∠3=180°.

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

m∠1=180°-m∠2=m∠3 m∠1=180°-m∠2=m∠3.

Therefore,

∠1≅∠3 ∠1≅∠3.

You can use a similar argument to prove that ∠2≅∠4 ∠2≅∠4. In the figure,

∠1≅∠3 ∠1≅∠3 and ∠2≅∠4 ∠2≅∠4.

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