Question

E and F are point on the PQ and PR respectively a triangle PQR for PE =3.9 cm, EQ = 3 cm, PF=3.6 cm and FR=2.4 cm check whether EF || QR. start yes or no​

Answer 1

Answer:SOLUTION :

(i)Given :

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

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

∴ PE/EQ = 3.9/3 = 39/30 = 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 || QR.

[By Converse of basic proportionality theorem]

(ii) Given :  

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 || QR.

[By Converse of basic proportionality theorem]

(iii) Given :

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

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  

And, PE/FR = 0.36/2.20 = 36/220 = 9/55  

∴ PE/EQ = PF/FR.

Hence, EF || QR.

[By Converse of basic proportionality theorem]

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