if all the three altitudes of a triangle are equal prove it is iscoseles triangle

Asked by  | 8th Dec, 2013, 08:32: PM

Expert Answer:

Given, AD, BE and CF are the attitudes 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 attitude)

∴ BC × AD = AB × CF = CA × BE

BC = AB = CA (Since, AD = BE = CF)

Hence, ΔABC is an equilateral triangle.

 

Answered by  | 8th Dec, 2013, 09:07: PM

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