Question

prove that the meridians of an equilateral triangle are equal​

Answer 1

Answer:

A median divides a side into two equal parts. In triangle AEC and triangle ABD we have. By SAS congruency criterion we get, ... Hence proved that medians of an equilateral triangle are equal.

Answer 2

Answer:

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.