Q. 23.5( 10 Votes )

If the length of three medians of a triangle are equal. Let us prove that the triangle is an isosceles triangle.

Answer :


In Δ BGD and Δ CGE,


BGD = CGE (vertically opposite angles) …(1)


BE = DC (medians are equal)


Since, centroid divides the median in ratio 2:1


So, and


BG = CG (as BE = DC) …(2)


And and


GE = DG (BE = DC) …..(3)


Hence, by SAS congruency, Δ BGD and Δ CGE are congruent.


By CPCT, BD = EC


2× BD = 2 × EC


AB = AC


Hence, the triangle is isosceles.


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