Question

If the three altitudes of a triangle are equal then prove that the triangle is an equilateral triangle.... PlZZ tell mE thiS QuE... ​

Answer 1

Answer:

Step-by-step explanation:

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.

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