Question

Abcd is a rectangle and pqrs are midpoints of ab, bc, cd, da respectively length of diagonal of rectangle is 8 cm the quadrilateral pqrs is

Answer 1

Answer:

Rhombus

Step-by-step explanation:

Given that ABCD is a rectangle and P, Q, R and S are the mid-points of AB, BC, CD and DA respectively.  

Now join points AC and BD as shown in the figure.

Now in ΔABC,

since P and Q are the mid points of AB and BC, then from mid point theorem

PQ || AC and PQ = AC ..........1

Now in ΔADC,

since S and R are the mid points of AD and CD, then from mid point theorem

SR || AC and SR = AC ..........2

From equation 1 and 2, we get

PQ || SR and PQ  = SR ....3

So quadrilateral ABCD is a parallelogram.

Now  

PS || QR and PS = QR ......4        (Opposite side of parallelogram)

Now in ΔBCD,

since Q and R are the mid points of BC and CD, then from mid point theorem

QR || BD and QR = BD ..........5

Again diagonal of a rectangle are equal.

So AC = BD .........6

From equation 1 ,2 ,3 4,,5 and 6, we get

PQ = QR = RS = SP

Hence PQRS is a rhombus.