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.

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

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

Prove that if one angle of a triangle is equal to the sum of the other two angles, the triangle is right angled.

If the ratio of the volumes of two spheres is 1:8, then the ratio of their surfaces area is

Prove that the areas of the equilateral triangle described on the side of a square is equal to half the area of the equilateral triangle described on one of its diagonal.

Prove that the sum of any two sides of a triangle is greater than twice the median drawn to the third side.

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

Prove that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

If the volumes of two spheres are in the ratio 6: 27, find the ratio of their surfaces areas.