Question

In $\Delta ABC$, D is a point on AB and E is a point on AC. If $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle ADE$ = $\angle ACB$, then $\Delta ABC$ is_____ triangle.

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

Answer 1

The correct option is B an isosceles

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".