Question

ABC is an equilateral triangle.D,E,F are points on BC,CA,AB respectively such that BD=CE=AF.Prove that triangle DEF is an equilateral triangle​

Answer 1

Answer:

Step-by-step explanation:

ABC is an equilateral triangle

∠A = ∠B = ∠C = 60°

AB = BC = AC

AF = BD = CE  

AB - AF = BC - BD = AC - CE

BF = CD = AE

Comparing

ΔAFE = ΔBDF = ΔCED

AF = BD = CE

AE = BF = CD

∠A = ∠B = ∠C = 60°

=> ΔAFE ≅ ΔBDF ≅ ΔCED

=> FE = DF = ED

=> Δ DEF is an equilateral Triangle