Question

ABC AB = BC Draw a bisector BD in an equilateral triangle. Prove that BD is median and high.

Answer 1

Explanation:

Given:-

AB = AC

Also , BD and CE are two medians

Hence ,

E is the midpoint of AB and

D is the midpoint of CE

Hence ,

1/2 AB = 1/2AC

BE = CD

In Δ BEC and ΔCDB ,

BE = CD [ Given ]

∠EBC = ∠DCB [ Angles opposite to equal sides AB and AC ]

BC = CB [ Common ]

Hence ,

Δ BEC ≅ ΔCDB [ SAS ]

BD = CE (by CPCT)