2017 · Q78
In a triangle PQR, X is a point on PR and Y is a point on QR such that PR = 10 cm, RX = 4 cm, YR = 2 cm, QR = 5 cm. Which one of the following is correct ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AXY is parallel to PQ
- BPQ = 2XY
- CPX = QY
- DPQ = 3XY
Explanation
RX/XP = 4/6 = 2/3 and RY/YQ = 2/3 (since PX = 10−4 = 6, QY = 5−2 = 3). Equal ratios on the two sides mean XY ∥ PQ by the converse of the basic proportionality theorem. Hence option (A). (Note option (C) is numerically false: PX = 6 ≠ 3 = QY.)