Question

In quadrilateral $ ACBD$, $ AC=AD$ and $ AB$ bisect $ \angle A$ (see Fig.) . Show that $ \Delta ABC \cong \Delta ABD$. What can you say about $ BC$ and $ BD$?

Answer 1

Prove the result $\Delta ABC\cong \Delta ABD$

Given that,

1. $AC=AD$
2. $\angle CAB=\angle DAB$[$\mathbf{\because }AB$ bisects $\angle A$]

In $\Delta ABC\&\Delta ABD,$

$AC=AD$

$AB$ is the common side

$\angle CAB=\angle DAB$

Therefore, $\Delta ABC\cong \Delta ABD$ [By SAS congruency]

$\therefore BC=BD$ v[By CPCT]

Hence, $BC$ and $BD$ are of equal lengths