Question

Prove that the diagonals of a rectangle are equal. [3 MARKS]

Answer 1

Concept : 1 Mark
Proof : 2 Marks



Consider a rectange $ABCD$

$AD=BC$ and $AB=CD$ [ Opposite sides of a rectange]

$\angle A=\angle B=\angle C=\angle D={90}^{\circ }$

$\Rightarrow {BD}^2$ = ${AD}^2$+ ${AB}^2$ --------(i)

and ${AC}^2$ = ${AB}^2$ + ${BC}^2$

$\Rightarrow {AC}^2={AB}^2$+ ${AD}^2$ --------(ii) [ since $BC=AD$ ]

From (i) and (ii) ${AC}^2$ = ${BD}^2$

$\Rightarrow AC=BD$

Hence, the diagonals of a rectangle are equal.