Question

prove that the median of an equilaterial triangle are equal​

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

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Step-by-step explanation:

we given the Question:-

prove that the median of an equilaterial triangle are equal.

Then solve:-

Let ABC be the equilateral triangle.

Then we have,

angle A=60°

angle B=60°

angle C=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. .............equation(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.......................... equation(2)

Similarly we can prove,

triangle ABD congruent to triangleAFC

Then,

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

By eq2 and eq3 we get,

AE=CF=BD

Hence,

proved that medians of an equilateral triangle are equation.