Question

ABCD is a trapezium in which AB II DC and AD = BC. If P, Q, R, S be respectively the mid-points of BA, BD and CD, CA. Then PQRS is a:

(First prove that it is rhombus and then prove that it is not a square)

Plz Help​

Answer 1

Answer:

Step-by-step explanation:

In the triangle ABC, P and Q are mid points of AB and AC respectively.

PQ || BC and PQ = 1/2

BC .. (1)

In ΔADC, QR = 1/2

AD = 1/2

BC ... (2)

Now we will consider ΔBCD,

SR = 1/2

BC.. (3)

In ΔABD,

PS = 1/2

AD = 1/2

BC.. (4)

So from (1), (2), (3) and (4)

we will get

PQ = QR = SR = PS

All sides are equal so PQRS is a Rhombus.