Question

state and prove alternate angle therom​

Answer 1

Step-by-step explanation:

Since k∥l , by the Corresponding Angles Postulate ,

∠1≅∠5 .

Therefore, by the definition of congruent angles ,

m∠1=m∠5 .

Since ∠1 and ∠2 form a linear pair , they are supplementary , so

m∠1+m∠2=180° .

Also, ∠5 and ∠8 are supplementary, so

m∠5+m∠8=180° .

Substituting m∠1 for m∠5 , we get

m∠1+m∠8=180° .

Subtracting m∠1 from both sides, we have

m∠8=180°−m∠1           =m∠2 .

Therefore, ∠2≅∠8 .

You can prove that ∠3≅∠5 using the same method.

The converse of this theorem is also true; that is, if two lines k and l are cut by a transversal so that the alternate interior angles are congruent, then k∥l .