Question

AF, BD and CE of triangle ABC are equal prove that triangle ABC is an equilateral triangle

Answer 1

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× BC × AD = 1/2 × AB × CF =1/2 × CA × BE (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.

Answer 2

Answer:

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Step-by-step explanation:

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× BC × AD = 1/2 × AB × CF =1/2 × CA × BE (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