Question

Use a paragraph proof to prove the alternate interior angles theorem.

Given: segment A B is parallel to segment C D.

Prove: Alternate interior angles are congruent

Answer 1

@ganeshie8

Answer 2

start by whats given

Answer 3

Since it is given that \(AB || CD\), `angle 2` and `angle 6` are congruent by corresponding angles postulate.

Answer 4

Also the vertical angles `angle 4` and `angle 2` are congruent as all vertical angles are equal. That makes `angle 4 = angle 6` by transitive property of equality. Hence the alternate interior angles are congruent.

Answer 5

QED.

or, you may conclude by saying that you can prove `angle 3 = angle 5` using similar argument.

Answer 6

Essentially paragraph proof is same as a two column proof - Only the presentation is different - Content is same.

Answer 7

ok thanks again ganesh

Answer 8

yw