triangle ABC is an equilateral triangle ABC is divided into three parts by points B and C is triangle ABC congruent to triangle AEC
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triangle ABC is an equilateral triangle ABC is divided into three parts by points B and C is triangle ABC congruent to triangle AEC
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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 equ