Question

AD,BE and CF,the altitude of triangle ABC are equal.Prove that triangle ABC is an equilateral triangle..

Answer 1

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• In triangle ABE and triangle ACF

BE=CF (Given)

∠A=∠A (Common)

∠AEB=∠AFC=90°

By AAS congruent rule ABE ≅ ACF

AB=AC (CPCT)

Similarly

BCF ≅ ABD

AB=BC

AC=BC

AB=AC

AB = BC = AC..... Proved

©© The triangle is a equaliteral triangle ©©

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Answer 2

See, area(abc)=0.5×ad×bc
area(ABC)=0.5×be×ac
area(ABC)=0.5×cf×ab
So all three are equal
As cf=be=ad
Area(ABC)=0.5×cf×ab=0.5×cf×ac=0.5×cf×bc
So we will get ab=BC
=ac
So it is equilateral