Question

in rohmbus ABCD show that 4AB2=AC2+BD2

Answer 1

First you draw a rhombus ABCD and diagonals AC and BD.

since the diagonals of rhombus bisect each other at 90 degree. therefore AO = AC/2 and BO = BD/2

In triangle AOB , AO2 + BO2 = AB2

AC2/4 +BD2/4 = AB2

AC2 + BD2 =4 AB2