Question

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Answer 1

GIVEN: ABCD is a rhombus

TO PROVE: AB^2 +BC^2 + CD^2 +DA^2=AC^2+BD^2

PROOF:

In triangle AOB ,

AB^2 = OA^2 + OB^2

Since OA = 1/2AC & OB = 1/BD

AB^2 = (AC/2)^2 + (BD/2)^2

AB^2 = AC^2/4 + BD ^2 /4

4 AB^2 = AC^2 + BD ^2 ----- 1

Since ABCD is a rhombus

AB = BC = DC = DA ------- 2

By sustituting 2 in 1 we have ,

AB^2 + BC^2 + CD^2 + DA^2 = AC ^2 + BD ^2

HENCE PROVED!!!

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