SOLUTION: I am trying to write a proof for a Geometry problem and can not figure the proof out. Given triangle ABC is equilateral then prove m<A=60 degree, m<B=60 degreee, m<C=60 degree. I

Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: I am trying to write a proof for a Geometry problem and can not figure the proof out. Given triangle ABC is equilateral then prove m<A=60 degree, m<B=60 degreee, m<C=60 degree. I      Log On

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Question 62782: I am trying to write a proof for a Geometry problem and can not figure the proof out. Given triangle ABC is equilateral then prove m
Answer by jai_kos(139) About Me  (Show Source):
You can put this solution on YOUR website!
Consider an equilateral triangle,
all the sides are equal.
Let the all the sides of triangle = 1cm
And A be the angle of the first side,
B be the third angle for the second side.
c be the second angle for the third side
Now we know the sine rule,
SinA / first side = Sin B /second side = SinC /third side
SinA /1 = sinB / 1 = Sin C/1
SinA =SinB =SinC
A =B=C
We know that the sum of the triangle is equal to 180 degree,
angleA+ angleB + angle C = 180
Since all the angles are same,
We write the above equation as,
3angle A = 180
angle A =180 /3 = 60
Angle A =angleB=Anglec= 60
or measure of A = 60
measure of B =60

measure of c = 60