Question

In $△$PQR, E and F are points on the sides PQ and PR respectively. Verify EF || QR. Given that PE = 4 cm, QE = 4.5 cm, PF = 8 cm and FR = 9 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 $PE=4\text{cm}$, $QE=4.5\text{cm}$, $PF=8\text{cm}$ and $FR=9\text{cm}$.

Using the basic proportionality theorem, we have

$\frac{PE}{EQ}=\frac{4}{4.5}=0.88\frac{PF}{FR}=\frac{8}{9}=0.88$

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

Hence, $EF$ is parallel to $QR$.