Question

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

Answer 1

answer is in the given fig

Answer 2

We have to prove that BD = CE when AB = AC. ( where BD and CE are the medians)


In ∆ ABC

AB = AC ( Isosceles ∆)

∠B = ∠C…………..(1)

[ANGLE OPPOSITE TO EQUAL SIDES ARE EQUAL]

AB = AC


1/2 AB = 1/2 BC

BE = CD…………(2)

( as BD and CE are the medians of a triangle)


In ΔEBC & ΔDCB

∠B = ∠C ( From eq I)

BC = CB (Common)

BE= CD (From eq 2)


ΔEBC ≅ ΔDCB ( by SAS congruency)


BD = CE (CPCT)


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


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Hope this will help you...