Question

if pqrs is a square then show that pr = qs​

Answer 1

Answer:

Solution :- In triangle POQ,

OP + OQ > PQ __(1)

Since sum of two sides is greater than 3rd sides.

In triangle QOR,

OQ + OR > QR ___(2)

Since sum of two sides is greater than 3rd sides.

In triangle SOR,

OS + OR > RS ___(3)

Since sum of two sides is greater than 3rd sides.

In triangle POS,

OP + OS > PS ___(4)

Since sum of two sides is greater than 3rd sides.

On adding all 4 equations we get,

OP + OQ + OQ + OR + OR + OS + OS + OP > PQ + PR + RS + PS

( OP + OR ) + ( OP + OR ) + ( OQ + OS ) + ( OQ + OS ) > PQ + PR + RS + PS

PR + PR + QS + QS > PQ + PR + RS + PS

PQ + PR + RS + PS > 2 (PR+QS)

\textbf{ \large{ Q.E.D }}  Q.E.D 

Answer 2

Answer:

if pqrs is square then all sides are equal and each angle is at 90 degree and diagnal are equal as it is property of square so pr= Q's mark me brainlist