Question

E and F are points on the sides pq and pr respectively of a ∆pqr.for each of the following cases,state whether a EF || QR :

(i) PE = 3.9cm, EQ=3cm, PF=3.6 and FR=2.4cm



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Answer 1

Answer :

• EF and PR aren't parallel .

GivEn :

We are given with a ΔPQR, where,

• PE = 3.9 cm

• EQ = 3 cm

• PF = 3.6 cm

• FR = 2.4 cm

ExplaNation :

We have to prove that EF || PR,

Also, we know that, if any line divides any 2 sides of the triangle in the same[equal] ratio , then the line is parallel to the 3rd side .

Before proving EF || PR , let's prove ,

➜ PE/EQ = PF/FR

Here,

• Consider line PEQ,

⇛ PE/EQ = 3.9/3

⇛ PE/EQ = 39/30

⇛ PE/EQ = 13/10

• Consider line PFR

⇛ PF/FR = 3.6/2.4

⇛ PF/FR = 36/24

⇛ PF/FR = 3/2

From the above 2 cases, we can observe that,

➜ PE/EQ ≠ PF/FR

Hence, EF and PR aren't parallel .