Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the third side of the triangle.

Prove that the circle drawn with any one of the equal sides of an isosceles triangle as diameter bisects the unequal side.

Prove that the two circles drawn on the two equal sides of an isosceles triangle as diameters pass through the mid point of the third side.

Prove that the medians to the two equal sides of an isosceles triangle are equal.

Prove that the angles opposite to equal sides of an isosceles triangle are equal.

Prove that if two medians of any triangle be equal, then it is an isosceles triangle.

Prove that the perpendiculars drawn from the vertices of equal angles of an isosceles triangle to the opposite sides are equal.

Prove that the bisector of the vertical angle of an isosceles triangle bisects the base at right angles.

With the help of Thales' theorem prove that the line drawn through mid-point of one side of a triangle parallel to another side bisects the third side.

Find the area of an isosceles triangle having the base xcm and one side ycm