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Converse of Pythagoras theorem : In a tr...

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.

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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.

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.

Knowledge Check

  • In a traingle, if square of one side is equal to the sum of the squares of other two sides, then the angle opposite the fitst side is :

    A
    `60^(@)`
    B
    `90^(@)`
    C
    `45^(@)`
    D
    `30^(@)`

  • 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 :

    A
    `60^@`
    B
    `90^@`
    C
    `45^@`
    D
    `30^@`

  • 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,

    A
    Pythagoras theorem
    B
    Thales theorem
    C
    Converse of Thales theorem
    D
    Converse of Pythagoras theorem

    • Similar Questions

    Explore conceptually related problems

    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.

    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-angled triangle, the square of hypotenuse is equal to the sum of the square of remaining 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.

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