Question

Show that diagonal of a rhombus intersect at right angle​

Answer 1

in triangle POS and ROS

op=oR (it is given )

os=os (it is common side)

angle POS=angle ROS(SAS rule)

hence PS =RS(CPCT)

but, they are adjacent sides and diagonals PR and Q's bisect each other

therefore PQRS is a parallelogram

it implies PQRS is rhombus

Answer 2

Let the rhombus be ABCD

AB=AD

also,diagonals bisect each other

DO=OB

AO is common so,triangle AOD=triangleAOB

SO,angle AOD=angle AOB....C.P.C.T

But angle AOD+angle AOB=180

so,angle AOD=angle AOB=90