Prove that that s triangle which has one of the angle as `30^0` cannot have all vertices with integral coordinates.

Prove that that s triangle which has one of the angle as 30^(@) cannot have all vertices with integral coordinates.

Show that the triangle which has one of the angles as 60^(@) can not have all verticles with integral coordinates.

A right triangle cannot have an obtuse angle.

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 eq. units, then the number of elements in the set S is

Let "S" be the set of all triangles in the xy-plane,each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates .If each triangle in "S" has area "60" sq.units,then the number of elements in the set "S" are

Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Prove that the coordinates of the vertices of an equilateral triangle can not all be rational.

Prove that of all the triangles with a given base and a given vertex angle, an isosceles triangle has the greatest bisector of the vertex angle.

(i) A triangle cannot have more than one right angle.