Question

State interior angle 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 . So, in the figure below, if k∥l , then ∠2≅∠8 and ∠3≅∠5 . Proof.

Answer 2

Answer:

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

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

Two parallel lines cut by a transversal n, with angles labeled 1 through 8

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.

mark me as brainliest