Question

Which of the following is not true for the figure below?

• A. AC $\perp$ BD
• B. ABCD is a kite
• C. $\angle ADB$ = $\angle ABD$
• D. $\angle DAB$ = $\angle DCB$

Answer 1

The correct option is D

$\angle DAB$ = $\angle DCB$

It is given that AB = AD and BC = CD.
Since, two pairs of adjacent sides are equal, the ABCD is a kite.

According to the properties of a kite:

$AC\perp BD$
[Diagonals of kite are perpendicular.]


In $\Delta ABD,$
$\angle ADB$ = $\angle ABD$ $[\because BA=DA$ and angles opposite to equal sides are equal$]$

But, $\angle DAB$ $\ne$ $\angle DCB$