Question

Prove that the medians corresponding to equal sides of an isosceles triangle are equal.

Answer 1

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


In ∆ ABC

AB = AC ( Isosceles $\Delta$)

$\angle$ B = $\angle$C…………..(1)

[ANGLE OPPOSITE TO EQUAL SIDES ARE EQUAL]

AB = AC


$\frac{1}{2}$ AB = $\frac{1}{2}$ BC

BE = CD…………(2)

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


In $\Delta$EBC & $\Delta$DCB

$\angle$B = $\angle$C ( From eq I)

BC = CB (Common)

BE= CD (From eq 2)


$\Delta$EBC $\cong$ $\Delta$DCB ( by SAS congruency)


BD = CE (CPCT)


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