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# ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that: (ii) diagonal BD bisects ∠ B as well as ∠ D.

Q : 8    ABCD is a rectangle in which diagonal AC bisects $\small \angle A$ as well as $\small \angle C$. Show that:

(ii) diagonal BD bisects $\small \angle B$ as well as $\small \angle D$.

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In $\triangle$ ADB,

AD = AB          (ABCD is a square)

$\angle$5=$\angle$7.................1(angles opposite to equal sides are equal )

$\angle$5=$\angle$8.................2 (alternate angles)

From 1 and 2, we have

$\angle$7=$\angle$8.................3

and        $\angle$7 =$\angle$6.................4(alternate angles)

From 1 and 4, we get

$\angle$5=$\angle$6.................5

Hence, from 3 and 5, diagonal BD bisects angles B as well as angle D.

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