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∠2m∠2 from both sides of both equations, we get
m∠1=180°−m∠2=m∠3m∠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.