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.

Theorem 6.8 : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

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.

PYTHAGORAS THEOREM : In a Right angled triangle; the square of hypotenuse is equal to the sum of the squares of the other two sides.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

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 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.

(Pythagoras's Theorem) Prove by vector method that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.