Question

ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.​

Answer 1

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!!]