Question

In the adjoining figure, if \(\dfrac{AD}{BD} = \dfrac{AE}{EC}\) and \(\angle BDE = \angle CED\), prove that \(\triangle ABC\) is an isosceles triangle.

Hint:

Use the Basic Proportionality Theorem and congruence rules for triangle equality.

Answer 1

Given: \[ \frac{AD}{BD} = \frac{AE}{EC} \] and \(\angle BDE = \angle CED\) By applying Basic Proportionality Theorem (Thales' theorem) and congruence criteria, we can prove \(\triangle ABD \cong \triangle CBE\) Therefore: \[ AB = AC \] Hence, \(\triangle ABC\) is isosceles.