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CGP EDU Academic Team
Published on: August 13, 2026
Prove using vectors : If two medians of a triangle are equal, then it is isosceles.
Text Solution
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Let ABC be a triangle and let BE and CF be two equal medians. Taking A as the origin, let the
position vectors of B and C be 
and 
respectively. Then,
P.V. of E = 
and P.V. of F = 
∴ 
= 
⇒ 
= 
Now, BE = CF ⇒ 
= 
⇒ 
= 
⇒ 
= 
⇒ 
= 
⇒ 
= 
⇒ 
. 
= 
. 
⇒ 
– 
+ 
= 
– 
+ 
⇒ 
– 
+ 4 
= 
– 
+ 
⇒ 3 
= 3 
⇒ 
= 
⇒ AB = AC Hence triangle ABC is an isosceles triangle.
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