how to do proofs

Question

in a triangle, segment AB is parallel to segment CD, and segment AC is parallel to segment BD. prove that triangle ABC is congruent to triangle DCB.

 

Answer 1

Hi Sara,

Though it's difficult to determine without a picture, I believe you have a parallelogram with vertices A, B, C, and D. Your goal is to prove triangle ABC congruent to triangle DCB.

How do you get there?

Well, given that you have some sets of parallel lines, and that you have to prove triangles congruent, chances are you'll use some of the angle relationships for two lines cut by a transversal.

Angles ABC and angles DCB are alternate interior angles (AB || CD and BC is the transversal), and are therefore congruent.

Angles ACB and DBC are also alternate interior angles and therefore congruent. (This time, it's because AC || BD , with BC as the transversal.)

Finally, BC is congruent to CB (itself) by the reflexive property.

You now can prove the two triangle congruent by SAS.