Question

prove that the median corresponding to equal sides of an isosceles triangle are equal​

Answer 1

Answer:

Step-by-step explanation:

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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