In Delta ABC,A-P-B,A-Q-C and overline{PQ} par | vedclass

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Question

(B) Given that in $\Delta ABC$,$\overline{PQ} \parallel \overline{BC}$.By the Basic Proportionality Theorem (Thales Theorem),we have $\frac{AP}{PB} =

Vedclass · Accepted Answer

$\frac{PQ}{BC} = \frac{AQ}{AC}$

Vedclass · Answer

(B) Given that in $\Delta ABC$,$\overline{PQ} \parallel \overline{BC}$.By the Basic Proportionality Theorem (Thales Theorem),we have $\frac{AP}{PB} = \frac{AQ}{QC}$.Also,since $\Delta APQ \sim \Delta ABC$ by $AA$ similarity criterion (as $\angle APQ = \angle ABC$ and $\angle AQP = \angle ACB$ due to parallel lines),the ratios of their corresponding sides are equal:$\frac{AP}{AB} = \frac{AQ}{AC} = \frac{PQ}{BC}$.Comparing the options,$\frac{PQ}{BC} = \frac{AQ}{AC}$ is correct.

In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overline{PQ} \parallel \overline{BC}$. Then,$\ldots \ldots \ldots$ holds good.

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