Question

Q.1 Prove that the madians of an equilateral triangle are equal.

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Answer 1

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Let ABC be the given equilateral △.

Then the things that we ,

∠.A=60°

∠.B=60°

∠C=60°

And ,

AB=BC=AC

and let AE , BD and CF be the medians.

we know that

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 △ AEC and △ABD we have.

AC=AB

∠.C=∠.A

EC=AD (from eq..1)

By SAS congruency criterion we get,

△ AEC congruent to △ABD.

By CPCT we get,

AE=BD..........................................................(2)

Similarly we can prove,

△ ABD congruent △ AFC

Then,

BD=CF..........................................................(3)

By eq2 and eq3 we get,

AE=CF=BD

Hence,

it is proved that the medians of equilateral triangle are equal

Answer 2

hope it helps..thanks