SOLUTION: a triangle XYZ has vertices X (1,1), y(3,1) and Z(2,4). Show that the triangle is an equilateral triangle

Question 938786: a triangle XYZ has vertices X (1,1), y(3,1) and Z(2,4). Show that the triangle is an equilateral triangle
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
an equilateral triangle is a triangle in which

are
if a triangle has vertices
at (,),
at (,) and
at (,)
to show that the triangle is an equilateral triangle, show that the distance between each two points is same
use distance formula to find the length of the all three sides

As and are equal,the triangle is an triangle , and (by definition) an isosceles triangle is a triangle with (at ) two equal sides

an triangle is a triangle with with all sides equal
an triangle is therefore a special case of an triangle having not just two, but all three sides and angles equal

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