Question

What do you call a parallelogram which has equal diagonals?

• A. A trapezium
• B. A rectangle
• C. A rhombus
• D. A kite

Answer 1

Answer: (B)

A rectangle

$\Rightarrow$ A parallelogram which has equal diagonals are called rectangle.

$\Rightarrow$ Trapezium, rhombus and kite does not contain equal diagonal.

$\Rightarrow$ Proof for rectangle contains equal diagonals are given below :-

$\Rightarrow$ In given figure ABCD is a rectangle.

$\Rightarrow$ In $△$ABC and $△$DCB

$\Rightarrow$ BC = CB [Common]

$\Rightarrow$ AB = DC [Opposite sides of rectangle]

$\Rightarrow$ $\angle$ABC = $\angle$DCA = 90${}^{\circ }$ [Each angle of rectangle is 90${}^{\circ }$]

$\Rightarrow$ $△$ABC $\cong$ $△$DCB [By SAS property]

$\therefore$ AC = BD [By CPCT]