Question
Measures of some angles in the figure are given. Prove that $\frac{AP}{PB} = \frac{AQ}{QC}$
✓
Answer
Here, PQ||BC (∵ ∠ APQ≅ ∠ ABC)(PROPERTY: If a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel)
∴ By Basic Proportionality Theorem
(Theorem : If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the same proportion.)
$\Rightarrow \frac{AP}{PB} = \frac{AQ}{QC}$
∴ By Basic Proportionality Theorem
(Theorem : If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the same proportion.)
$\Rightarrow \frac{AP}{PB} = \frac{AQ}{QC}$
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