Exercise 11 Page 465

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, $△OMN$ is a right triangle, where $\angle MON$ is a right angle and $\overline{OP}$ is the altitude to the hypotenuse. Having verified the necessary conditions, we can write the similarity statements. Finally, we can combine these three similarity statements into one. Note that there are many possible correct combinations for writing this statement — the triangle names could be written in any order and the names of the triangle could be written in any order.