abcd is the rhombus prove that 4AB2 = AC2+BD2
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in rhombus abcd
AB=BC=CD=AD
AO=1/2AC
BO=1/2BD
in ∆ABO
AB2=AO2+BO2
AB2=(1/2AC)2 + (1/2BD)2
AB2=AC2/4 + BD2/4
AB2= AC2+BD2/4
by cross multiplying
4AB2=AC2+BD2
AB=BC=CD=AD
AO=1/2AC
BO=1/2BD
in ∆ABO
AB2=AO2+BO2
AB2=(1/2AC)2 + (1/2BD)2
AB2=AC2/4 + BD2/4
AB2= AC2+BD2/4
by cross multiplying
4AB2=AC2+BD2
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