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    Question

    In a triangle PQR, S is a point on the side QR such that

    PS⊥QR, then which of the following options is true?
    A PS² + PR² = PQ² + QR² Correct Answer Incorrect Answer
    B PR² + QS² = PQ² + SR² Correct Answer Incorrect Answer
    C PQ² + PR² = QS² + SR² Correct Answer Incorrect Answer
    D PS² + QS² = PQ² + PR² Correct Answer Incorrect Answer

    Solution

    Since PS is perpendicular to QR, PS acts as the height from vertex P to the base QR in the right triangle PSQ and PSR. In △PSQ (right triangle): PQ² = PS² + QS² (by Pythagoras) In △PSR (right triangle): PR² = PS² + SR² (by Pythagoras) Adding these two equations: PQ² + PR² = (PS² + QS²) + (PS² + SR²) Simplifying: PQ² + PR² = 2PS² + QS² + SR² Since S is a point on QR: QS + SR = QR Therefore, PR² + QS² = PQ² + SR²

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