Question

PQ = 1.28 cm; PR = 2.56 cm,
PM =0.16 cm; PN =0.32 cm.

Answer 1

PQ = 1.28, PM =0.16
$\Rightarrow$ MQ = PQ - PM = 1.28 - 0.16 = 1.12
NR = PR - PN = 2.56 - 0.32 = 2.24
Now

$\frac{PM}{MQ}=\frac{0.16}{1.12}=\frac{1}{7}$

$\frac{PN}{NR}=\frac{0.32}{2.24}=\frac{1}{7}$

$\therefore \frac{PM}{MQ}=\frac{PN}{NR}$ $[Eachratio=\frac{1}{7}]$
$\Rightarrow$ By the converse of Basic Proportionality Theorem,
$MN\parallel QR$