Prove of theorem related to isosceles triangle

Area of an isosceles triangle

Prove that of all triangles on the same base and of the same area,the isosceles triangle has the least perimeter.

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 base.

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

In the given figure, (AD)/(DB)=(AE)/(EC) and angle ADE=angle ACB . Prove that Delta ABC is an isosceles triangle.

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral, so formed is cyclic.

Lines of symmetry of an isosceles triangle

Study the given and prove that DeltaPQR is an isosceles triangle.

Prove that median from the vertex of an isosceles Triangle is the bisector of the vertical angle