Having given the bases and the sum of the areas of a number of triangles which have a common vertex, show that the locus of the vertex is a straight line.

Which two triangles have angle B as common ?

If on a given base B C , a triangle is described such that the sum of the tangents of the base angles is m , then prove that the locus of the opposite vertex A is a parabola.

Find the area of an equilateral triangle having altitude h cm.

Find the area of an isosceles triangle having base a cm and one side b cm.

If two isosceles triangles have a common base, prove that the line segment joining their vertices bisects the common base at right angles.

The number of lines of symmetry which a triangle have is

The ends of the hypotenuse of a right angled triangle are (6, 0) and (0, 6). Find the locus of the third vertex.

One vertex of a triangle of given species is fixed and another moves along circumference of a fixed circle. Prove that the locus of the remaining vertex is a circle and find its radius.

The area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm, is :

If a tangent to the parabola y^2 = 4ax meets the axis of the parabola in T and the tangent at the vertex A in Y, and the rectangle TAYG is completed, show that the locus of G is y^2 + ax = 0.