In a rhombus ABCD the diagonals bisect at O. Prove that AC2 + BD2 = 4 AB2.
AnanyaSwamiBalihara:
is it "AC^2 ", "BD^2" and AB^2
"AB^2"
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In traingle ADC
AC^2=AD^2+DC^2.....(I)
In traingle BCD
BD^2=BC^2+DC^2.....(I)
adding crospondind side of both equation
AC^2+BD^2=AD^2+ DC^2+ BC^+ DC^2
=AB^2+ AB^2+ AB^2+ AB^2
=4AB^2 (all side of rombus are equal).
AC^2=AD^2+DC^2.....(I)
In traingle BCD
BD^2=BC^2+DC^2.....(I)
adding crospondind side of both equation
AC^2+BD^2=AD^2+ DC^2+ BC^+ DC^2
=AB^2+ AB^2+ AB^2+ AB^2
=4AB^2 (all side of rombus are equal).
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