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

AC $⊥$ BD

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ABCD is a kite

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$∠ A D B$ = $∠ A B D$

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$∠ D A B$ = $∠ D C B$

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Solution

The correct option is D
$∠ D A B$ = $∠ D C B$

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:

$A C ⊥ B D$
[Diagonals of kite are perpendicular.]

In $Δ A B D,$
$∠ A D B$ = $∠ A B D$ $[∵ B A = D A$ and angles opposite to equal sides are equal $]$

But, $∠ D A B$ $\neq$ $∠ D C B$

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