Question : In $\triangle$ABC, BD and CE are perpendicular to AC and AB respectively. If BD = CE, then $\triangle$ABC is:
Option 1: Equilateral
Option 2: Isosceles
Option 3: Right–angled
Option 4: Scalene
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Correct Answer: Isosceles
Solution :
Given: In $\triangle$ABC, BD and CE are perpendicular to AC and AB respectively.
BD = CE
The area of $\triangle ABC$ $=\frac{1}{2}\times{AB}\times {CE}$
The area of $\triangle ABC$ $=\frac{1}{2}\times{AC}\times {BD}$
$⇒\frac{1}{2}\times{AB}\times {CE}=\frac{1}{2}\times{AC}\times {BD}$
AB = AC (since, BD = CE)
So, $\triangle ABC$ is an isosceles triangle.
Hence, the correct answer is 'Isosceles'.
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