Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

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.

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

Prove that in a parallelogram, the sum of the squres of the diagonals is equal otthe four times the sum of the square of three conterminos edges.

Fill in the balnks : (i) In a right triangle, the square of the hypotenuse is equal to the……….of the square of the other two sides. (ii) If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is......... (iii) Of all the line segments that can be drawn to a given line form a given point outside it, the.............is the shortest.

Prove by vector method that the sum of the square of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

In a right angled triangle, five times the square on the hypotenuse is equal to four times the sum of the squares on the medians drawn from the acute angles. Prove it.

prove by vector method that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Prove analytically that the sum of square of the diagonals of a rectangle is equal to the sum of squares of its sides.