Question

in an isosceles triangle prove that 2medians are equal​

Answer 1

Let ABC be the equilateral triangle.

Then we have,

angle A=60°

angleB=60°

angleC=60°

and,

AB=BC=AC

and let AE , BD and CF be the medians.

A median divides a side into two equal parts.

AB=BC=AC

AF+BF=BE+CE=AD+CD

2AF=2BE=2AD

AF=BE=AD

therefore,

AF=BF=BE=CE=AD=CD............................1

In triangle AEC and triangle ABD we have.

AC=AB

angle C=angle A

EC=AD (from eq1)

By SAS congruency criterion we get,

triangle AEC congruent to triangle ABD.

By CPCT we get,

AE=BD..........................................................2

Similarly we can prove,

triangle ABD congruent to triangle AFC

Then,

BD=CF..........................................................3

By eq2 and eq3 we get,

AE=CF=BD

Hence proved that medians of an equilateral triangle are equal.