Question

Question 2 (iii)
E and F are points on the sides PQ and PR respectively of a $\Delta PQR$. For the following case, state whether EF || QR.
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm

Answer 1

In ΔPQR, E and F are two points on the sides PQ and PR respectively.
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm, PF = 0.36 cm
(Given) Here, EQ = PQ - PE = 1.28 - 0.18 = 1.10 cm;
FR = PR - PF = 2.56 - 0.36 = 2.20 cm
So, $\frac{PE}{EQ}=\frac{0.18}{1.10}=\frac{18}{110}=\frac{9}{55}...\left(i\right)$
And, $\frac{PE}{FR}=\frac{0.36}{2.20}$ = $\frac{36}{220}=\frac{9}{55}...\left(ii\right)$
$\therefore \frac{PE}{EQ}=\frac{PF}{FR}$.
Hence, EF is parallel to QR.