ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.
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To Prove:-
- BD = CE
Given:-
- AB = AC
- Also , BD and CE are two medians
Step-by-step explaination:-
Hence ,
- E is the midpoint of AB and
- D is the midpoint of CE
Hence ,
- 1/2 AB = 1/2AC
- BE = CD
In ∆ BEC and ∆ CDB ,
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!!]
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