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 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)

$△$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.