Question

if altitude of a triangle are equal then prove that the given triangle is an equilateral triangle​

Answer 1

Given,

AD, BE and CF are the altitudes drawn on sides BC, CA and AB of Δ ABC such that AD = BE = CF

Area of Δ ABC = 1/2 x BC × AD = 1/2 × AB × CF = 1/2 × CA × BE

(Since, Area of Δ = 1/2 × Base × Correspondence altitude)

∴ BC × AD = AB × CF = CA × BE

BC = AB = CA (Since, AD = BE = CF)

Hence, ΔABC is an equilateral triangle.

Hence proved.

Answer 2

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