When square is inscribed how to identify the similar triangles

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In the picture, $ \square PQRS $ is a square inscribed in a right triangle. How can we come to conclusion that $ \triangle ABC \sim \triangle PBQ $? My understanding is that $ \triangle ABC $ and $ \triangle PBQ $ have one angle in common which is the right angle. What could be the other angle which is congruent so that we can apply AA property.

I have gone through several questions and explanations but couldn't find on what basis $ \triangle ABC $ and $ \triangle PBQ $ are similar.

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1 Answer

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For this to be true, $PQRS$ doesn't even need to be a square: any parallelogram will do. Because $PQ \parallel RS$, we also have $PQ \parallel AC$, so line $AB$ makes the same angle with $PQ$ as with $AC$. This gives us another equal angle.

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