MCQ
In the given figure, if $\text{AB}\parallel\text{DC}$ then $AP$ is equal to :
- A$6\ cm.$
- B$7\ cm.$
- C$5.5\ cm.$
- ✓$5\ cm.$
✓
Answer
Correct option: D.
$5\ cm.$
In tiangles $\text{APB}$ and $\text{CPD}.$
$\angle\text{APB}=\angle\text{CPD} \ [$Vertically opposite angles$] $
$ \angle\text{BAP}=\angle\text{ACD}$ Alternaet angles as $\text{AB}\parallel\text{CD}$
$\therefore\triangle\text{APB}\sim\triangle\text{CPD} \ [\text{AA}$ similarity$]$
$\therefore\frac{\text{AB}}{\text{CD}}=\frac{\text{CP}}{\text{AP}}$
$\Rightarrow\frac{4}{6}=\frac{\text{AP}}{7.5}$
$\Rightarrow\text{AP}=\frac{7.5\times4}{5\text{ cm}}$
$\angle\text{APB}=\angle\text{CPD} \ [$Vertically opposite angles$] $
$ \angle\text{BAP}=\angle\text{ACD}$ Alternaet angles as $\text{AB}\parallel\text{CD}$
$\therefore\triangle\text{APB}\sim\triangle\text{CPD} \ [\text{AA}$ similarity$]$
$\therefore\frac{\text{AB}}{\text{CD}}=\frac{\text{CP}}{\text{AP}}$
$\Rightarrow\frac{4}{6}=\frac{\text{AP}}{7.5}$
$\Rightarrow\text{AP}=\frac{7.5\times4}{5\text{ cm}}$
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