Question

ln the given figure ABC is an isosceles triangle with AB=AC . BD and CE are two medians of the triangle. prove that BD = CE.

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Answer 1

$\huge\sf{\underline{\underline{➪Sᴏʟᴜᴛɪᴏɴ \: :-}}}$

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 !!!!