Question
In $\triangle\text{ABC},$ points P and Q are on CA and CB, respectively such that CA = 16cm, CP = 10cm, CB = 30cm and CQ = 25cm. Is PQ || AB?
✓
Answer
Given: AC = 16cm, CP = 10cm, CB = 30cm and CQ = 25cm, we get
We will check whether $\frac{\text{CP}}{\text{AC}}=\frac{\text{CQ}}{\text{BC}}$ or not to conclude whether PQ || AB.
$\frac{\text{CP}}{\text{AC}}=\frac{10\text{cm}}{16\text{cm}}=\frac{5}{8}$
$\frac{\text{CQ}}{\text{CB}}=\frac{25\text{cm}}{30\text{cm}}=\frac{5}{6}$
$\therefore\frac{\text{CP}}{\text{AC}}\neq\frac{\text{CQ}}{\text{CB}}$
Hence, PQ is not parallel to AB.
We will check whether $\frac{\text{CP}}{\text{AC}}=\frac{\text{CQ}}{\text{BC}}$ or not to conclude whether PQ || AB.
$\frac{\text{CP}}{\text{AC}}=\frac{10\text{cm}}{16\text{cm}}=\frac{5}{8}$
$\frac{\text{CQ}}{\text{CB}}=\frac{25\text{cm}}{30\text{cm}}=\frac{5}{6}$
$\therefore\frac{\text{CP}}{\text{AC}}\neq\frac{\text{CQ}}{\text{CB}}$
Hence, PQ is not parallel to AB.
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