Question

E and F are points on the sides PQ and PR respectively of a triangle PQR. For each of the following cases, state whether EF || QR:
(1) 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
(ii) PQ=1.28 cm, PR=2.56 cm, PE=0.18 cm and PF=0.36 cm
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Answer 1

Answer:

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Answer 2

Answer:-

★ Given:-

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

★ Note:- Look into the attechment for the diagram.

(i) Given:-

• PE = 3.9 cm
• EQ = 3 cm
• PF = 3.6 cm
• FR = 2,4 cm

Therefore, using BPT, we get:-

PE/EQ = 3.9/3 = 39/30 = 13/10 = 1.3

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) Given:-

• PE = 4 cm
• QE = 4.5 cm
• PF = 8cm
• RF = 9cm

★ Using BPT :-

PE/QE = 4/4.5 = 40/45 = 8/9

And, PF/RF = 8/9

So, we get here,

PE/QE = PF/RF

Hence, EF is parallel to QR.

(iii) Given:-

• PQ = 1.28 cm
• PR = 2.56 cm
• PE = 0.18 cm
• PF = 0.36 cm

EQ = PQ – PE = 1.28 – 0.18 = 1.10 cm

FR = PR – PF = 2.56 – 0.36 = 2.20 cm

PE/EQ = 0.18/1.10 = 18/110 = 9/55 → (i)

PE/FR = 0.36/2.20 = 36/220 = 9/55 → (ii)

So, we get:-

PE/EQ = PF/FR

Hence, EF is parallel to QR.