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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. Only (i) and (iii)
Given that
△PQR will be an isosceles triangle.
O is an interior point of ΔPQR such that ∠OPR = ∠ORP
So, OP = OR
Hence, Ist statement is true.
O is the centroid of △PQR, is not found, so the second statement is false.
△ PQO ≅ △RQO with the condition (Side side side) PO = OR, PQ = RQ, OQ = OQ
So, statement iii is also true.
Hence, Only (i) and (iii) are correct