If I enter the mosque and the Imam is prostrating, or sitting between the two prostrations, or in the Tashahhud, do I join him and say another "Allahu Akbar" for the prostration or the sitting after the opening "Takbirat al-Ihram"?

If a worshiper enters while the Imam is prostrating, he should say the opening takbir (Allahu Akbar) and join him. This rak'ah (unit of prayer) will not be counted for him because he did not catch the bowing.

Scholars have differed concerning the takbir of the congregant who joins the Imam while he is prostrating or sitting. Some said that he should descend without saying takbir, while others said that he should descend while saying takbir. The precautionary approach is to say the takbir.

If the congregant begins the prayer while the Imam is prostrating, and the Imam raises his head before the congregant places his forehead on the ground, then the congregant should raise his head with the Imam and not prostrate.

If he catches him in the first prostration, he should descend and prostrate with him. When the Imam raises his head and sits between the two prostrations, the congregant should sit with him, and then prostrate with him for the second prostration.