Question

3. ABCD is a rectangle and P, Q, R and S are mid-points of the sideAB, BC,CD,DA
respectively. Show that the quadrilateral PQRS is a rhombus.​

Answer 1

Step-by-step explanation:

W .k.t

diagonals of rectangle are equal to each other

AC=BD –(a)

In triABC ,P & Q are the mid points of the sides AB &BC respectively

therefore,using mid point thm-

PQllAC,PQ =1/2 AC

In triADC,S &R are the mid points of the sides AD &DC respectively

therefore,using mid point thm–

SR=1/2AC

we get, PQ=SR=1/2AC –(b)

In triABC, S&P are the mid points of AD&BA respectively

therefore using mid point thm–

SP=1/2BD

in triBDC ,R&Q are the midpoints of DC &BC respectively

therefore using mid point thm-

RQ=SR=1/2BD

RQ=SR=1/2BD=1/2AC –from(a)–(c)

from (b )&(c)we get RQ=SR=PQ=SR

It is a rhombus