Theorem 6.9 : In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

If in a triangle, square of one side is equal to the sum of squares of the other two sides, then the angle opposite the first side is :

Rahul is studying in X Standard. He is making a kite to fly it on a Sunday. Few questions came to his mind while making the kite. Give answers to his questions by looking at the figure In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This theorem is called as,

Converse of Pythagoras theorem: In a triangle; If the square of one side is equal to the sum of the squares of the other two sides. then the angle opposite to the side is a right angle.

In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, prove that the angle opposite to the first side is a right angle. Use the above theorem to find the measure of anglePKR in Fig. 7.52.

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.

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 a right triangle with the angle opposite the first sides as right angle.

Prove that is a right angle triangle, the square of the hypotenuse is equal the sum of the squares of other two sides.

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

Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Use the above theorem, in the following. If ABC is an equilateral triangle with AD bot BC , then prove that AD^(2) = 3DC^(2) .