Question

ABCD is a parallelogram in which P Q R and S are midpoints of side ab BC CA and ad respectively prove that pqrs is a rhombus​

Answer 1

$\textbf{\underline {\underline { Solution:}}}$

in the Parallelogram ABCD

AP=BP.

DR=CR.

DS=AS.

BQ=CQ.

=Now add all :-

=AP+DR+DS+BQ=BP+CR+AS+CQ.

=Now take common the similar Sides :-

=(AP+BP)(DR+CR)=(AS+DS)(BQ+CQ)

=Now cut the same sides :-

=AB+DR=AD+BC.

=Now we have : 2AB=2BC.

=We know that in a Parallelogram opposite sides are equal so :

=AB=DC=DA=CB.[opposite sides are equal]

=Hence the Given Parallelogram is a rhombus .