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E and F are points on the sides PQ and ...

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 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

Text Solution

Verified by Experts

(i) As per data,
`PE = 3.9, EQ = 3, PF = 3.6 and FR = 2.4`
By basic proportionality theorem,
`(PE)/(EQ) = 3.9/3=1.3`
`(PF)/(FR) = 3.6/2.4 = 1.5`
hence, both are not equal,
Thus, EF is not parallel to QR
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