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    Question

    In ΔPQR,PQ=QR and O is an interior point of ΔPQR such

    that ∠ OPR= ∠ ORP . Consider the following statements: (i) ΔPOR is an isosceles triangle. (ii) O is the centroid of ΔPQR. (iii) ΔPQO is congruent to ΔRQO. Which of the above statements are correct?
    A Only (i) and (ii) Correct Answer Incorrect Answer
    B Only (i) and (iii) Correct Answer Incorrect Answer
    C Only (ii) and (iii) Correct Answer Incorrect Answer
    D Only (ii) Correct Answer Incorrect Answer

    Solution

    △PQR will be an isoceles triangle, so Ist statement is true. O is the centroid of △PQR, is not found, so second statement is false. △ PQO ≅ △RQO with the condition (Side side side) PO = OR PQ = RQ OQ = OQ So, statement iii, is also true.

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