can you please solve this problem
5&6
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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
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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