prove that the medians bisecting the equal sides of an isosceles triangle are also equal

now, here we have to prove that  BD = CE when AB = AC. ( where BD and CE are the medians)

now, in ΔEBC and ΔDCB,

we have 

AB = AC

=> 1/2 AB = 1/2 BC

=>  BE = CD ( BE = CD = 1/2AB = 1/2BC as BD and CE are the medians of a triangle) ....... (1)

now, BC = CB

and, ∠EBC = ∠DCB

hence, by SAS congruency,

ΔEBC ≅ ΔDCB

now, by congruent parts of congruent triangles property,

BD = CE

so, we have proved that medians bisecting the equal sides of an isosceles triangle are also equal.

hope it helps!!

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