Prove that the area of a rhombus is equal to half of the product of the diagonals.

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

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.

Prove that a cyclic rhombus is a square

Prove that the area of a trapezium is half the sum of the parallel sides multiplied by the distance between them.

Square of the resultant of two forces of equal magnitude is equal to three times the product of their magnitude. The angle between them is

Show that the diagonals of a rhombus are perpendicular to each other.

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

Show that the magnitude of a vector is equal to the square root of the scalar product of the vector with itself .

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

Show that the diagonals of a rhombus divide it into four congruent triangles.