Question

$ABC$ and $DBC$ are two isosceles triangles on the same base $BC$. Then $\angle ABD=\angle ACD$.

• A. True
• B. False

Answer 1

The correct option is A True

$\Delta ABC$ is an isosceles triangle

Thus, $\angle ABC=\angle ACB$ ..... $\left(1\right)$

Similarly, $\Delta DBC$ is an isosceles triangle

Thus, $\angle DBC=\angle DCB$ ..... $\left(2\right)$

Adding $\left(1\right)$ and $\left(2\right),$ we get

$\angle ABC+\angle DBC=\angle ACB+\angle DCB$

$\Rightarrow \angle ABD=\angle ACD$