Answer :

(i)**Given :PE = 3.9 cm,**

**EQ = 3 cm,**

**PF = 3.6 cm,**

**FR = 2.4 cm**

Now we know,

Triangle **Proportionality Theorem:** If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

So, if the lines EF and QR are to be parallel, then ratio PE:EQ should be proportional to PF:PR

Therefore, EF is not parallel to QR

(ii)

We know that,

Triangle **Proportionality Theorem:** If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Hence,

Therefore, EF is parallel to QR

(iii)

In this we know that,

Triangle **Proportionality Theorem:** If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

So, if the lines EF and QR are to be parallel, then ratio PE:EQ should be proportional to PF:PR

Hence,

EF is parallel to QR

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