Question

prove that the medians of an equalateral triangle are equal

Answer 1

Let ABC be an equilateral triangle.

Also let D,E,F be the mid points of BC, AC and AB respectively.

So,AD,BE and CF are the medians of the triangle ABC.

All angles in a equilateral triangle are equal.

So, angle A=B=C=60°

In triangle ADC and ABE,

★BC/2=AC/2
DC=AE

★Angle C=A [60°]

★AC=AB

Triangle ADC ≅ Triangle ABE

AD=BE (C.P.C.T)

Similarly,

BE=CF

Therefore, AD=BE=CF

So,all medians of an equilateral triangle are equal.

Hence proved.

Answer 2

Answer:

Step-by-step explanation: