Question

ABCD is a rectangle and P, Q, R and S are midpoint of the sides AB, BX, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.​

Answer 1

PQ || RS and PQ = RS

In PQRS,

one pair of opposite side is parallel nad equal.

Hence, PQRS is a parallelogram.

Answer 2

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Step-by-step explanation:

Here we are joining A and C.

In triangle ABC,

P is the mid point of AB

Q is the mid point of BC

PQ||AC

PQ=1/2 AC

In triangle ADC

R is mid point of CD

S is the mid point of AD

RS||AC

RS=1/2AC

So,PQ||RS and PQ=RS

AP=BP

angle PAS=angleBPQ

AS=BQ

ΔAPS=ΔBPQ

PQ=RS=PS=PQ

hence proves it is a rhombus