Question

Write the statement of alternate angles test.​

Answer 1

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent .

FOR EXAMPLE:

So, in the figure below, if k ∥ l , then ∠2≅∠8 and ∠3≅∠5

Proof :

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