Question
E and F are points on the sides PQ and PR respectively of a ∆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.
Solution
(i) We have,
From (i) and (ii), we have
Therefore, EF is not parallel to QR [By using converse of Basic proportionality theorem]
(ii) We have,
From (i) and (ii), we have
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Therefore,
[Using converse of Basic proportionality theorem]
(iii) We have,
From (i) and (ii), we have
Therefore,
[Using converse of Basic proportionality theorem]
From (i) and (ii), we have
Therefore, EF is not parallel to QR [By using converse of Basic proportionality theorem]
(ii) We have,
From (i) and (ii), we have
Therefore,
[Using converse of Basic proportionality theorem]
(iii) We have,
From (i) and (ii), we have
Therefore,
[Using converse of Basic proportionality theorem]
