Question 7 of 14intermediate🔧 ApplyShort Answer3 marks

E and F are points on the sides PQ and PR respectively of a Δ PQR. 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 = 0.36 cm

(i)

State whether EF ∥ QR when PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm

Answer

EF is not parallel to QR

(ii)

State whether EF ∥ QR when PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

Answer

EF is parallel to QR

(iii)

State whether EF ∥ QR when PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm

Answer

EF is parallel to QR

Explanation

This question applies the converse of Basic Proportionality Theorem (Theorem 6.2): If a line divides two sides of a triangle in the same ratio, then it is parallel to the third side. For EF to be parallel to QR, we need to verify if PE/EQ = PF/FR in each case.