2. E and F are points on the sides PQ and PR, respectively of a ΔPQR. For each of the following cases, state whether EF || QR. (i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm

(i) To determine if EF is parallel to QR, we need to check if the ratios of the corresponding sides are equal. This is based on the Converse of Basic Proportionality Theorem (or Thales Theorem) which states that if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Here, we need to check if PE/EQ = PF/FR. Substituting the given values, we get 3.9/3 = 3.6/2.4. Simplifying both sides, we get 1.3 = 1.5. Since the ratios are not equal, EF is not parallel to QR.

(ii) Similarly, we check if PE/QE = PF/RF. Substituting the given values, we get 4/4.5 = 8/9. Simplifying both sides, we get 0.89 = 0.89. Since the ratios are equal, EF is parallel to QR.

(iii) Here, we don't have the lengths of EQ and FR. We only have the lengths of PE and PF. So, we can't apply the Converse of Basic Proportionality Theorem directly. We need more information to determine if EF is parallel to QR.