Question

State true or false:
In the give figure, $AC=AE,AB=AD$ and $\angle BAD=\angle EAC$.

Then $BC=DE$.

A. True

B. False

Answer 1

The correct option is A (True)

Its given that $AC=AE,AB=AD$ and

Consider $\angle BAD=\angle EAC$
Adding $\angle DAC$ on boths sides,
$\Rightarrow \angle BAD+\angle DAC=\angle EAC+\angle DAC$
$\therefore \angle BAC=\angle DAE$......(i)

From $△ABC$ and $△ADE$

$AB=AD$

$\angle BAC=\angle DAE$ and $AC=AE$

From SAS Criteria, we say that $△ABC\cong △ADE$

From the property of corresponding parts of congruent triangle are equal, we say that $BC=DE$ .