Question

In a $\Delta ABC$, the internal bisector of $\angle A$ meets opposite side BC at D. Through vertex C, line CE is drawn parallel to DA which meets BA produced at point E. Which of the following is true?

• A. $\Delta ACE$ is isosceles
• B. $\Delta ACE$ is equilateral
• C. $\Delta ACE$ is scalene
• D. $\Delta ACE$ is right angled

Answer 1

The correct option is A

$\Delta ACE$ is isosceles

Given: $AD\parallel EC$,
$\angle BAD=\angle DAC$

$\angle BAD=\angle AEC$ [Corresponding angles] ..... (1)

$\angle DAC=\angle ACE$ [Alternate angles] ..... (2)

And we know that $\angle BAD=\angle DAC$,

So, $\angle AEC=\angle ACE$

$\Rightarrow \Delta AEC$ is isosceles triangle.