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CEMC Gauss (Grade 8), 2010

Geometry Difficulty 2.0 Junior Find the answer Canada

In $\triangle PQR$ , a line segment is drawn from $P$ to point $S$ on side $QR$ . If $\triangle PQS$ and $\triangle PRS$ have the same area, which of the following statements must be true?

(A) $PQ = PR$ (B) $PS = PQ$ (C) $QR = PS$ (D) $QS = SR$ (E) $PQ = QR$

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