Show that the points : `(a,a),(-a,-a),(sqrt(3)a,-sqrt(3)a)` 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.

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

Show that A(a,b,c),B(b,c,a) and C(c,a,b) are the vertices of an equilateral triangle.

Show that the points (2,4,3),(4,1,9) and (10,-1,6) are the vertices of an isosceles right angled triangle.

Show that the points : A (0,1,2),B(2,-1,3) and C (1,-3,1) are vertices of an isosceles right angle triangle.

Show that the points (3, 4), (8, -6) and (13, 9) are the vertices of a right angled triangle.

Without using the pythagorus, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

Show that the following sets of points are the vertices of an equilateral triangle :- (a,a) , (-a ,-a) and (sqrt3a, -sqrt3a) .

Show that the following sets of points are the vertices of an equilateral triangle :- (1, 1),(- 1,-1) and (-sqrt3,sqrt3) .

Show that the following sets of points are the vertices of an equilateral triangle :- (3a,5a) , (3a+sqrt(3a),6a) and (3a,7a) .