✅Answer: Please pay attention to the following narrations:

1 عَنْ مُحَمَّدِ بْنِ مُسْلِمٍ عَنْ أَبِي جَعْفَرٍ قَالَ: إِذَا أَدْرَكْتَ التَّكْبِيرَةَ قَبْلَ أَنْ يَرْكَعَ الْإِمَامُ فَقَدْ أَدْرَكْتَ الصَّلَاةَ.

📚 Al-Tahdhib, Vol. 3, p. 43

Imam Baqir (peace be upon him) said: If you reach the takbir (of ruku') before the Imam goes into ruku', you have certainly caught the prayer!

2 عَنْ سُلَيْمَانَ بْنِ خَالِدٍ عَنْ أَبِي عَبْدِ اللَّه أَنَّهُ قَالَ: فِي الرَّجُلِ إِذَا أَدْرَكَ الْإِمَامَ وَ هُوَ رَاكِعٌ وَ كَبَّرَ الرَّجُلُ وَ هُوَ مُقِيمٌ صُلْبَهُ ثُمَّ رَكَعَ قَبْلَ أَنْ يَرْفَعَ الْإِمَامُ رَأْسَهُ فَقَدْ أَدْرَكَ الرَّكْعَةَ.

📚 Al-Tahdhib, Vol. 3, p. 43

Imam Sadiq (peace be upon him) said: If a person reaches the Imam while he is in ruku' and the person says the takbir while standing straight, and then goes into ruku' before the Imam raises his head from ruku', he has certainly caught that rak'ah!

3 عَنِ الْحَلَبِيِّ عَنْ أَبِي عَبْدِ اللَّه أَنَّهُ قَالَ: إِذَا أَدْرَكْتَ الْإِمَامَ وَ قَدْ رَكَعَ فَكَبَّرْتَ وَ رَكَعْتَ قَبْلَ أَنْ يَرْفَعَ الْإِمَامُ رَأْسَهُ فَقَدْ أَدْرَكْتَ الرَّكْعَةَ وَ إِنْ رَفَعَ رَأْسَهُ قَبْلَ أَنْ تَرْكَعَ فَقَدْ فَاتَتْكَ الرَّكْعَةُ.

📚 Al-Faqih, Vol. 1, p. 389

Imam Sadiq (peace be upon him) said: If you reach the congregational Imam while he has gone into ruku', and you say the takbirat al-ihram and go into ruku' before the Imam raises his head, you have caught that rak'ah. And if he raises his head from ruku' before you go into ruku', that rak'ah has been missed by you!

4 عَنْ مُعَاوِيَةَ بْنِ مَيْسَرَةَ عَنْ أَبِي عَبْدِ اللَّه أَنَّهُ قَالَ: إِذَا جَاءَ الرَّجُلُ مُبَادِراً وَ الْإِمَامُ رَاكِعٌ أَجْزَأَتْهُ تَكْبِيرَةٌ وَاحِدَةٌ لِدُخُولِهِ فِي الصَّلَاةِ وَ الرُّكُوعِ.

📚 Al-Faqih, Vol. 1, p. 407

Imam Sadiq (peace be upon him) said: When a person comes in a hurry and the congregational Imam is in ruku', one takbir is sufficient for him to enter the prayer and to go into ruku'!

5 أَحْمَدُ بْنُ عَلِيِّ بْنِ أَبِي طَالِبٍ الطَّبْرِسِيُّ فِي الْإِحْتِجَاجِ عَنْ مُحَمَّدِ بْنِ عَبْدِ اللَّهِ بْنِ جَعْفَرٍ الْحِمْيَرِيِّ عَنْ صَاحِبِ الزَّمَانِ أَنَّهُ كَتَبَ إِلَيْهِ يَسْأَلُهُ عَنِ الرَّجُلِ يَلْحَقُ الْإِمَامَ وَ هُوَ رَاكِعٌ فَيَرْكَعُ مَعَهُ وَ يَحْتَسِبُ بِتِلْكَ الرَّكْعَةِ فَإِنَّ بَعْضَ أَصْحَابِنَا قَالَ إِنْ لَمْ يَسْمَعْ تَكْبِيرَةَ الرُّكُوعِ فَلَيْسَ لَهُ أَنْ يَعْتَدَّ بِتِلْكَ الرَّكْعَةِ فَأَجَابَ إِذَا لَحِقَ مَعَ الْإِمَامِ مِنْ تَسْبِيحِ الرُّكُوعِ تَسْبِيحَةً وَاحِدَةً اعْتَدَّ بِتِلْكَ الرَّكْعَةِ وَ إِنْ لَمْ يَسْمَعْ تَكْبِيرَةَ الرُّكُوعِ.

📚 Al-Ihtijaj, p. 488

Humairi wrote a letter to Imam Mahdi (may Allah hasten his reappearance) and asked about a person who reaches the congregational Imam while he is in ruku' and performs ruku' with him and counts that rak'ah; because one of the companions said: If he does not hear the takbir of ruku', he cannot count that rak'ah!

The Imam wrote in response: If he catches one tasbih of the tasbihs of the Imam's ruku', he counts that rak'ah, even if he has not heard the takbir of ruku'!

6 عَنْ مُحَمَّدِ بْنِ مُسْلِمٍ قَالَ: قَالَ أَبُو عَبْدِ اللَّه إِذَا لَمْ تُدْرِكْ تَكْبِيرَةَ الرُّكُوعِ فَلَا تَدْخُلْ فِي تِلْكَ الرَّكْعَةِ.

📚 Al-Kafi, Vol. 3, p. 381

Imam Sadiq (peace be upon him) said: If you do not catch the takbir of ruku', do not enter that rak'ah!

✅ Although in a few narrations, such as narration 6, it is stated that if a person does not catch the takbir of ruku' with the congregational Imam, he should not enter that rak'ah, it is explicitly stated in many other narrations that if the follower reaches the congregational prayer and the Imam is in ruku', while he is standing completely straight, he should say a single takbir to start the prayer and go into ruku'. If he catches one tasbih of the Imam's ruku' tasbihs, or if he reaches the state of ruku' (reaching the fingertips to the knees for a man and the hands to the top of the knees on the thighs for a woman) before the congregational Imam raises his head from ruku', he has caught that rak'ah and counts it. And if the congregational Imam raises his head from ruku' before the follower reaches the state of ruku', the follower has not caught that rak'ah, and therefore he continues the prayer with the Imam, but he counts the next rak'ah as his first rak'ah, not the second!

اللَّهُمَّ فَصَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ