There are two situations about this problem. The second one looks different, but it is exactly the same as the auxiliary line, almost the same. Let me talk about the idea of the theme (this idea applies to two cases): both cases need CN and CM, but after calculating the length of both ends, one adds up to get MN, and the other difference gets MN. The length of CN is exactly the same in both cases. The key is to find CM, and the key to find CM is to prove that m is the midpoint of ad'

Let's make a vertical line through a and d' to CM and its extension line. As long as these two vertical lines are equal, it proves that m is the midpoint. Through the congruence of triangle, it is easy to prove that the length of these two vertical lines is equal to the length of CN.

One is △ AQC △ CNB and the other is △ D' PC △ CNE'.