# ABCD is a rhombus. AC and BD are its two diagonals intersecting at O. Prove that AB^2 + BC^2 + CD^2 + DA^2 = AC^2 + BD^2?

##### 1 Answer

May 10, 2018

Please see the explanation.

#### Explanation:

The sides of rhombus are congruent by definition, the diagonals that are perpendicular bisectors divide the figure into 4 congruent right triangles, se we can conclude the followings:

But:

Also:

So:

Thus:

Hence proved.