Prove that the points `(5,3,2),(3,2,5) and (2,5,3)` are the vertices of an equilateral triangle.

show that the points A(1,-1,-5), B(3,1,3) and C(9,1,-3) are the vertices of an equilateral triangle.

The points (3,7),(6,5) and (15,-1) are the vertices of an equlateral triangle

Show that the points (1,-2,-3),(2,-3,-1) and (3,-1,-2) are the vertices of an equilateral triangle

Prove that the points (2a,4a),(2a,6a) and (2a+sqrt(3)a,5a) are the vertices of an equilaterall triangle whose side is 2a

Prove that the points (2,-2), (-2, 1) and (5, 2) are the vertices of a right angled triangle. Also find the area of this triangle.

Prove that the points A(2, 4), B(2, 6) and C(2 + sqrt(3) , 5) are the vertices of an equilateral triangle.

Prove that the points (3,-2),(4,0),(6,-3) and (5,-5) are the vertices of a parallelogram.

Show that the points A(1,2),B(1,6), C(1 + 2sqrt(3),4) are the vertices of an equilateral triangle .

Prove that the points (0, 0), (3, (pi)/(2)) and (3, (pi)/(6)) are the vertices of an equilateral triangle.

Prove that the points (5, -2), (-4, 3) and (10, 7) are the vertices of an isosceles right-angled triangle.