Is the rak'ah counted as complete if the worshiper catches the Imam during ruku'?

The congregant follows the Imam in the state he finds him in. So, if he comes to the prayer and the Imam is prostrating, he prostrates with him, and that is not counted as anything for him. Whoever catches the rak'ah has caught the prayer. However, the congregant does not catch the complete rak'ah unless he catches the bowing with the Imam. And whoever misses the bowing must make up a complete rak'ah.