arunitin
Consider a parallelogram ABCD, AB=CD AD=BC if AC=BD then consider triangleABC and triangleDCB here BC=BC AC=BD AB=DC therefore by SSS congruence we can prove that TriangleABC is congruent to triangle DCB By CPCT, angle ABC= angle DCB since they are in linear pair angle b+ angle c= 180° 2(angle b)=180° angle b= 180°/2 angle b =90° similarly all angles are 90° therefore it is a rhombus
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AB=CD
AD=BC
if AC=BD
then consider triangleABC and triangleDCB
here
BC=BC
AC=BD
AB=DC
therefore by SSS congruence
we can prove that
TriangleABC is congruent to triangle DCB
By CPCT,
angle ABC= angle DCB
since
they are in linear pair
angle b+ angle c= 180°
2(angle b)=180°
angle b= 180°/2
angle b =90°
similarly
all angles are 90°
therefore it is a rhombus