Question

ABC is an isosceles triangle with AB=AC AND BD,CE are it's two median . Show that BD=CE.

Answer 1

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 [ cpct ]
------> Proved !!!!