Question

prove that figure obtained by joining the midpoint of the adjacent sides of a rectangle is a rhombus ​

Answer 1

Step-by-step explanation:

The figure is shown below:

Let ABCD be a rectangle where P,Q,R,S are the midpoint of AB,BC,CD,DA. We need to show that PQRS is a rhombus

For help we draw two diagonal BD and AC as shown in figure Where BD=AC (Since diagonal of rectangle are equal)

Proof:

From △ABD and △BCD

PS=

2

1

BD=QR and PS∥BD∥QR

2PS=2QR=BD and PS∥QR .......(1)

Similarly 2PQ=2SR=AC and PQ∥SR ........(2)

From (1) and (2) we get

PQ=QR=RS=PS

Therefore PQRS is a rhomus.

Hence proved