Question

Given: AE = DE, AB = DC
Prove: ABE = DCE

Answer 1

Pythagoras theorem says A^2 + B^2 = C^2
In the context of this question, AE^2 - AB^2 is equivalent to saying DE^2 - DC^2
Therefore since AE^2 - AB^2 = BE^2, DE^2 - DC^2 = CE^2
So, BE^2 = CE^2
And ABE^2 = DCE^2
which is equivalent to saying ABE = DCE.
It will help if you read what I wrote while looking at the diagram.

Answer 2

Thanks a lot for the help. You explained it really well.