As we can see, △ OMN is a right triangle, where ∠ MON is a right angle and OP is the altitude to the hypotenuse. Having verified the necessary conditions, we can write the similarity statements.
△ OMN ~ △ PMO
△ PMO ~ △ PON
△ PON ~ △ OMN
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.
△ OMN ~ △ PMO ~ △ PON
