Question

In $△$PQR, E and F are points on the sides PQ and PR respectively. verify EF || QR. PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm, FR = 2.4 cm.

Answer 1

The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that $PE=3.9$ cm, $EQ=3$ cm, $PF=3.6$ cm and $FR=2.4$ cm.

Using the basic proportionality theorem, we have

$\frac{PE}{EQ}=\frac{3.9}{3}=1.3\frac{PF}{FR}=\frac{3.6}{2.4}=1.5$

Since $\frac{PE}{EQ}\ne \frac{PF}{FR}$

Hence, $EF$ is not parallel to $QR$.