Question

ABCD is a rectangle in which diagonal BD bisects $\angle B$. Then, ABCD is a square.

• A. True
• B. False

Answer 1

The correct option is A

True

ABCD is a rectangle .... (given)
BD bisects $\angle B$ ...(given)
Therefore $\angle ABD=\angle DBC={45}^{\circ }$
$\angle DAB={90}^{\circ }$
Therefore $\angle ADB={180}^{\circ }-{90}^{\circ }-{45}^{\circ }$
$={45}^{\circ }$
Hence, AD=AB ($△ADB$ is isosceles)
ABCD is a square (Adjacent sides of a rectangle are equal)