Question

Consider $\Delta$ ABC. If $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle$ ADE = $\angle$ ACB. Then $\Delta$ ABC is an equilateral triangle.

• A. True
• B. False

Answer 1

The correct option is B

False

Since, $\frac{AD}{DB}=\frac{AE}{EC}$ (Given)

So by Converse of Basic Proportionality theorem,
$DE\parallel BC$

Given, $\angle$ ADE = $\angle$ ACB ---- (1)
Also, $\angle$ ADE = $\angle$ ABC ----- (2) [Transverse angles in parallel lines are equal]

From (1) and (2),
$\Rightarrow \angle ABC=\angle ACB$
Hence, it is an isosceles triangle.