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 (2,4),(2,6) and (2+sqrt 3,5) are the vertices of an equilateral triangle.

Prove that the points A (1,2,3), B(2,3,1) and C(3,1,2) 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.

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 (2,2) (-2,-2) and (-2sqrt3, 2sqrt3) are the vertices of an equllateral 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 (0,0) (3, sqrt(3)) and (3, -sqrt(3)) are the vertices of an equilateral 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 (2a, 4a), (2a, 6a) and (2a+sqrt3a , 5a) are the vertices of an equilaterall triangle whose side is 2a