Question

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

• A. equilateral
• B. isosceles
• C. right angled
• D. scalene

Answer 1

The correct option is B

isosceles

From Converse of Basic Proportionality theorem,
Since $\frac{AD}{DB}=\frac{AE}{EC}$
$\therefore DE\parallel BC$.

Given $\angle ADE=\angle ACB$ ---- (1)
Since corresponding angles in parallel lines are equal, we have
$\Rightarrow \angle ADE=\angle ABC$ -----(2)

From (1) & (2),
$\Rightarrow \angle ABC=\angle ACB$
$⟹AB=AC$ $(\because \text{sides opposite to equal angles are equal})$

Hence it is an isosceles triangle.