E and F are points on the sides PQ and PR respectively of `DeltaP Q R`. 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
(ii) PE = 4 cm. QE = 4.5 cm. PF = S cm and RF = 9 cm
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm

Explanation

To determine whether the line segment EF is parallel to QR in each case, we can use the Basic Proportionality Theorem (also known as Thales' theorem). According to this theorem, if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

The theorem states that if EF || QR, then:

\[ \frac{PE}{EQ} = \frac{PF}{FR} \]

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