Question

Prove the similarity of \triangle ABC with respect to \triangle PQR.

Similarity
To prove: The similarity of $$\displaystyle\triangle{A}{B}{C}$$ with respect to $$\displaystyle\triangle{P}{Q}{R}$$.
Given information: Here, we have given that acute angles of both right angles are congruent ($$\displaystyle\Rightarrow\angle{A}{C}{B}\stackrel{\sim}{=}\angle{P}{R}{Q}$$)

Proof: In $$\displaystyle\triangle{A}{B}{C}\ {\quad\text{and}\quad}\ \triangle{P}{Q}{R}$$
$$\displaystyle\angle{A}{C}{B}\stackrel{\sim}{=}\angle{P}{R}{Q}$$ (Given)
$$\displaystyle\angle{A}{B}{C}\stackrel{\sim}{=}\angle{P}{Q}{R}$$ (Right Angles)
$$\displaystyle\Rightarrow\triangle{A}{B}{C}\sim\triangle{P}{Q}{R}$$ (By AA Similarity Rule)
$$\displaystyle\therefore$$ The triangles are similar.