Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

If the areas of two similar triangles are equal, prove that they are congruent.

Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : The ratio of the perimeters of two similar triangles is 4 : 25, then the ratio of their areas is……..

Prove that three times the square of any side of an equilateral triangle is equal to four times the square of the altitude.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

The ratio of the areas of the incircle and the circumcircle of a square is-

Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

If the ratio of the volume of two spheres is 64:27, then find the ratio of their surface area.

Write down the converse of following statements: If the sum of squares of two sides foa triangle is equal to the square of third side of a triangle, then the triangle is right angled.

The ratio of gravitational mass to inertial mass is equal to:

Prove that the medians of an equilateral triangle are equal.