Question

In $\Delta ABC$, $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle ADE$ = $\angle ACB$. Then $\Delta ABC$ is

• A. an equilateral triangle.
• B. an isosceles triangle.
• C. a right angled triangle.
• D. a scalene triangle.

Answer 1

The correct option is B an isosceles triangle.

From Converse of Basic Proportionality theorem,
Since $\frac{AD}{DB}=\frac{AE}{EC}⟹DE\parallel BC$.
Given $\angle$ ADE = $\angle$ ACB ---- (1)
Also $\angle$ ADE = $\angle$ ABC -----(2)
(Transverse angles in parallel lines are equal)
From (1) & (2),
$\Rightarrow \angle ABC=\angle ACB$
Hence it is an "isosceles triangle".