Q

# ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that: (i) ABCD is a square.

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

(i) ABCD is a square

Views

Given: ABCD is a rectangle with AB=CD and BC=AD $\angle$1=$\angle$2 and $\angle$3=$\angle$4.

To prove: ABCD is a square.

Proof :     $\angle$1=$\angle$4 .............1(alternate angles)

$\angle$3=$\angle$4 ................2(given )

From 1 and 2, $\angle$1=$\angle$3.....................................3

In $\triangle$ADC,

$\angle$1=$\angle$3          (from  3 )

DC=AD             (In a triangle, sides opposite to equal angle are equal )

A rectangle whose adjacent sides are equal is a square.

Hence, ABCD is a square.

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