Question

In ABC, medians BD and CE are equal and intersect each other at 0. Prove that ABC is an isosceles triangle.​

Answer 1

Given:-

BD and CE are two medians

To prove:-

Δ ABC is Isosceles Triangle

Proof:-

E is the midpoint of AB and

D is the midpoint of CA

Hence ,

1/2 AB = 1/2 ACBE = CD

In Δ BEC and ΔCDB ,

Hence,

1/2 AB = 1/2ACBE = 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 C.P.C.T.)

So,

Δ ABC is a Isosceles Triangle

Hence Proved

Answer 2

Answer:

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)