Question

pls it Cary 40 point



if all the three altitude of a triangle are equal the triangle equilateral. Prove it

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 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.

Ps- please ubderstand the diagram as am unable to post it cause of some reason.

Answer 2

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

hope its help you