Question

prove that the medians of equilateral triangles

Answer 1

Answer:

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

Step-by-step explanation:

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