Question

$ABC$ is a triangle in which altitudes $BE$ and $CF$ to sides $AC$ and $AB$ are equal.Then $△ABC$ is

• A. An Equilateral Triangle
• B. An Isosceles Triangle
• C. A Scalene Triangle
• D. None

Answer 1

The correct option is B An Isosceles Triangle

Given : $BE=CF$

In $△ABE$ and $△AFC$

$\angle AEB=\angle AFC={90}^{\circ }$

$\angle BAE=\angle CAF$ {$\angle A$ is common}

$BE=CF$ {Given}

$△ABE\cong △AFC$ {By AAS congruence}

$AB=AC$

$AE=AF$

So, $△ABC$ is isosceles triangle.