Prove that in a quadrilateral the sum of all the sides is greater than the sum of its diagonals.

Prove that in any quadrilateral the sum of the diagonals is greater than its semi—perimeter.

Prove that the sum of the sides of a quadrilateral is greater than twice of one of its diagonal.

Prove that the sum of the sides of a quadrilateral is greater than twice of one of its diagonal.

In which of the following quadrilateral sum of squares of all sides is equal to the sum of squares of diagonals?

Prove that in any parallelogram, the 'sum of the squares of all sides is equal to the sum of the squares of the diagonals'.

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Prove that the perimeter of a triangle is greater than the sum of its three medians.

Prove that the perimeter of a triangle is greater than the sum of its three medians.

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Prove that the perimeter of a triangle is greater than the sum of its altitudes.