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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
an equilateral triangle is a triangle in which all three sides are equal
if a triangle XYZ has vertices
X at (1,1),
y at (3,1) and
Z at (2,4)
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

XY=sqrt%28%283-1%29%5E2%2B%281-1%29%5E2%29+
XY=sqrt%282%5E2%2B0%29+
XY=sqrt%284%29
XY=2

YZ=sqrt%28%282-3%29%5E2%2B%284-1%29%5E2%29
YZ=sqrt%28%28-1%29%5E2%2B%283%29%5E2%29
YZ=sqrt%281%2B9%29
YZ=sqrt%2810%29
YZ=3.162277660168379


XZ=sqrt%28%282-1%29%5E2%2B%284-1%29%5E2%29
XZ=sqrt%281%2B9%29
XZ=sqrt%2810%29
XZ=3.162277660168379


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

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