Question

In $△ABC,$ the ratio of altitudes $BE$ and $CF$ is equal to one. What can be said about the nature of $△ABC?$

• A. Isoceles
• B. Equilateral
• C. Scalene
• D. Data is not enough

Answer 1

The correct option is A

Isoceles

Given: $BE=FC$

In $△ABE$ and $△ACF,$

$\angle A=\angle A$ [common angle]

$\angle AEB=\angle AFC={90}^{\circ }$
$BE=FC$ [given]

$\Rightarrow △ABE$ and $△ACF$ are congruent by $AAS$ property of congruence, because two angles and a side of one triangle are equal to corresponding two angles and a side of the other triangle.

Therefore, corresponding sides and angles will be equal.

So, $AB=AC.$ Therefore, $△ABC$ is an isoscles triangle.