Question

The figure formed by joining the mid points of the adjacent sides of a rectangle is a :

• A. Square
• B. Rhombus
• C. Trapezium
• D. Kite

Answer 1

The correct option is B Rhombus

The figure formed by joining the mid points of the adjacent sides of a rectangle is a rhombus
Given: ABCD is a rectangle, P, Q,R,S is the mid-point of AB,AD,DC,CB respectively.
To prove: $PQRS$ is a rhombus.
Proof:
Joint $PQ,QR,RS,ST$ (constructions)
$PQ=RS=0.5AC$
$PS=QR=0.5BD$ (Mid-point theorem)
$\Rightarrow$ $PQRS$ is a parallelogram ( The opposite sides of a quadrilateral areparallel and equal)
$AC=BD$ (the diagonals of a rectangle equal)
$\Rightarrow$ $PQ=RS=QR=PS$ (the half of the equal quantities equal)
$PQRS$ is a rhombus ( 4 sides are equal)