Measures of some

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.)

⇒