Question

E and F are points on the sides PQ and PR respectively of a ΔPQR. 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​

Answer 1

In APQR, E and F are two points on side PQ and PR respectively.

(i) PE = 3.9 cm, EQ = 3 cm (Given)

PF = 3.6 cm, FR = 2,4 cm (Given)

.. PE/EQ = 3.9/ 339/30 13/10 = 1.3 [By using Basic proportionality theorem]

And, PF/FR = 3.6/2.4 36/24 = 3/2 = 1.5

So, PE/EQ PF/FR

Hence, EF is not parallel to QR.

(ii) PE = 4 cm, QE 4.5 cm, PF = 8cm, RF = 9cm

..PE/QE = 4/4.5= 40/45 = 8/9 [By using Basic proportionality theorem]

And, PF/RF = 8/9

So, PE/QE PF/RF

Hence, EF is parallel to QR.

(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm, PF = 0.36 cm (Given)

Here, EQ PQ - PE 1.28 0.18 = 1.10 cm

And, FR = PR - PF 2.56 0.36 = 2.20 cm

So, PE/EQ = 0.18/1.10 18/110 = 9/55 ... (i)

And, PE/FR = 0.36/2.20 36/220 = 9/55 ... (ii)

.. PE/EQ = PF/FR.

Hence, EF is parallel to QR.