NCERT Solutions
Class 10 Maths
Triangles

Ex. 6.2 Q.2
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) Given, PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm,
therefore
PE/EQ = 3.9/3 = 3 cm
PF/FR = 3.6/2.4 = 36/24 = 3/2 = 1.5 cm
Since PE/EQ ≠ PF/FR
Hence, EF is not parallel to QR.

(ii) Given, PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
PE/EQ = 4/4.5 = 40/45 = 8/9 cm
PF/FR = 8/9 cm
Since PE/EQ = PF/FR
Hence, according to converse of Thales theorem, EF || QR.

(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm, therefore
PE/PQ = 0.18/1.28 = 18/128 = 9/64 cm
PE/PR = 0.36/2.56 = 36/256 = 9/64 cm

Since PE/PQ = PE/PR
Hence, according to converse of Thales theorem, EF || QR.