Question

$ABCD$ is rectangle in which diagonal $BD$ bisects $\angle B$ then, $ABCD$ is a

• A. square
• B. rectangle
• C. parallelogram
• D. trapezium

Answer 1

The correct option is A square

In $\Delta$BAD & $\Delta$BCD,

$\angle$ABD $=\angle$CBD given

$\angle A=\angle C$

and BD$=$BD common side

$\therefore \Delta$BAD $\cong$ $\Delta$BCD[by AAS congruency rule]

AB$=$BC

and AD$=$CD ……….$\left(1\right)$ [by CPCT rule)

But in rectangle ABCD, opposite sides are equal.

AB$=$CD

and BC$=$AD ………$\left(2\right)$

From $\left(1\right)$ & $\left(2\right)$

AB$=$BC$=$CD$=$DA

So, ABCD is a square.