Question

M and N are points on the sides PQ and PR respectively of a $\Delta PQR$. For each of the following cases state whether MN is parallel to QR
A. PM= 4, QM = 4.5, PN = 4, NR = 4.5
B. PQ= 1.28, PR= 2.56, PM = 0.16, PN= 0.32

• A. only in case A
• B. only in case B
• C. both in the case A & B
  
• D. None of these

Answer 1

The correct option is C both in the case A & B



Case I $\frac{PM}{QM}=\frac{4}{4.5}and\frac{PN}{NR}=4.5$
$\frac{PM}{PQ}=\frac{PN}{PR}=\frac{4}{9.5}$

Case II $\frac{PM}{PQ}=\frac{0.16}{1.28}$
And $\frac{PN}{PR}=\frac{0.32}{2.56}=\frac{0.16}{1.28}$
Hence, $\frac{PM}{PQ}=\frac{PN}{PR}$
Therefore MN is parallel to QR in both the cases (By converse of proportionality theorem)