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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

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B

Equilateral

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C

Scalene

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D

Data not enough

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Solution

## The correct option is A Isoceles Given: BE = FC In △ABE and △ACF, ∠A = ∠A (common angle) ∠AEB = ∠AFC = 90∘ 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.

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