2016 · Q80
In a triangle P Q R, point X is on P Q and point Y is on P R such that X P = 1.5 units, X Q = 6 units, P Y = 2 units and Y R = 8 units. Which of the following are correct?
- 1Q R = 5 X Y
- 2Q R is parallel to X Y.
- 3Triangle P Y X is similar to triangle PRQ.
Select the correct answer using the code given below.
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 and 2 only
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Explanation
PX/PQ = 1.5/7.5 = 1/5 and PY/PR = 2/10 = 1/5, so XY ∥ QR by the converse of the basic proportionality theorem (statement 2 true). Hence ΔPYX ∼ ΔPRQ (statement 3 true) with QR/XY = 5 (statement 1 true). So 1, 2 and 3, option D.