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The given triangle is a right triangle with an altitude to the hypotenuse.
△ PRQ ~ △ PQS ~ △ SQR
We want to write a similarity statement relating the three triangles in the given diagram. To do so we can use the Right Triangle Altitude Theorem.
This theorem tells us about the relationship between the similar right triangles contained in every right triangle that has an altitude to the hypotenuse. Now, let's analyze the given diagram.
As we can see, △ PRQ is a right triangle, ∠ PQR is a right angle, and SQ is the altitude to the hypotenuse. Having verified the necessary conditions, we can write the similarity statement. △ PRQ ~ △ PQS △ PRQ ~ △ SQR △ PQS ~ △ SQR
