Question

In a quadrilateral ABCD, if $\angle C=\angle B+\angle D$ and AB = AC, then AC =AD.

• A. True
• B. False

Answer 1

The correct option is A True

Given :

$AB=AC$

$\angle ABC=\angle ACB$

Also, $\angle BCD=\angle ABC+\angle ADC$ ( Since sides opposite to equal angles are equal).

Also, $\angle BCD=\angle ABC+\angle ADC$

$\angle ACB+\angle ACD=\angle ABC+\angle ADC$

$\angle ACB+\angle ACD=\angle ACB+\angle ADC$

$\angle ACD=\angle ADC$

i.e., $AC=AD$ ( Sides opposite to equal angles are equal).