SOLUTION: prove that the four triangles formed by diagonals of rhombus are congruent.

Algebra ->  Geometry-proofs -> SOLUTION: prove that the four triangles formed by diagonals of rhombus are congruent.       Log On


   

Question 1063775: prove that the four triangles formed by diagonals of rhombus are congruent.




Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

I will just give an outline of how to prove it. You
can write it up in a two-column proof.

A rhombus is a parallelogram with four congruent sides. 
So, all sides of rhombus ABCD are congruent. That is 

AB ≅ BC ≅ CD ≅ AD 

   
 
We also know that the diagonals of a parallelogram bisect 
each other. Since a rhombus is a parallelogram, it also has
this property. 

Therefore BE ≅ DE, AE ≅ CE.

Therefore all 4 triangles are congruent by SSS.

Edwin