Quadrilateral Proof

Question

Given: line AB is parallel to line CD and AB is congruent to CD

 

Prove: AE=EC

 

*Note: the diagram given looks like a parallelogram with both diagonals drawn

Answer 1

It's probably where the diagonals meet.

 

Angles AEB and DEC are congruent vertical angles.

 

Due to the parallel lines: ABC and DCB are congruent.

 

This forces angles BAD and ADC congruent because of the 180 degree triangle property.

 

AB congruent to CD is given.

 

So the triangles are congruent by ASA

 

AE = EC follows by CPCTC