Prove: triangle ABC is congruent to triangle DCB

Question

Given: Line AB is congruent to line CD

          Line AB is parallel to line CD

Answer 1

Hi Sarah, you can use the side, angle, side theorem to prove that triangle ABC is congruent to triangle DCB.

 

Given:

 

Line AB is congruent to line CD

Ling AB is parallel to line CD

 

Proof:

 

This gives something like this:

 

           C       D

---------\------------------- line CD

          /  \    /

        /     \  /

------------\---------------- line AB

     A         B

 

Since lines AB and CD are parallel, line BC becomes a transversal of the parallel lines.

 

Side 1: Given AB congruent to CD.

 

Angle: Angle ABC congruent to Angle BCD, alternate interior angles of a transversal through parallel lines are congruent.

 

Side 2: CB is congruent to CB, reflex property of congruent lines.

 

Therefore, triangle ABC is congruent to triangle DCB.

 

Questions?