There are two sets of two Surah’s in the Qur’an that are joint or connected to the extent that one cannot be recited without the other. When reading them, particularly in Salah, we must read them together. This means in some cases, we would be obliged to read three surah’s in a single rak’ah (cycle).

Hadiths

And it has been reported by Al Ayyashi by his chains from Al Mufazzal Bin Salih,
Abu Abdullah (As) said, ‘I heard him saying: ‘Do not join two Chapters in one Cycle (of Prayer) except for “[93:1] I swear by the early hours of the day” (Surah Ad-Duhaa), and “[94:1] Have We not expanded for you your breast” (Surah Ash-Sharh), and [105:1] “Have you not considered how your Lord dealt” (Surah Al-Fil) and “[106:1] For the protection of the Qureysh” (Surah Quraysh).

Source: Tafseer Noor al-Thaqalain, Volume 5, Page 675, Hadith #3 (See Image below)

And from Abu Al-Abbas,
from one of them (5th Or 6th. Imam (as)) having said: ‘[105:1] “Have you not considered how your Lord dealt” and “[106:1] For the protection of the Qureysh” is one Chapter’

Source: Tafseer Noor al-Thaqalain, Volume 5, Page 675-676, Hadith #4 (See Image below)

Untitled

This means Surah Ad-Duhaa and Surah Ash-Sharh are considered one joint Surah, and Surah Al-Fil and Surah Quraysh are considered one joint Surah.

Scholars

The scholars are in agreement, including Sayed al-Kho’i (hf). Here is the opinion of Sayed Sistani (hf):

987. In the the daily obligatory prayers, one should recite Surah al-Hamd in the first and second Rak’ats, and thereafter one should, on the basis of precaution, recite one complete Surah. The Surah az Zuha and Surah Inshirah are treated as one Surah in namaz, and so are the Surah al-Fil and Quraysh.

Link: http://www.sistani.org/english/book/48/2221/

Sayed Khomeini says in Tahrir al-Wasilah:

Problem # 6 Surat al-Fil (Chapter 105 of the Quran) and Surat al-Ilaf (Chapter 106 of the Quran) are treated as a single Surah, and so are Surat al-Duha (Chapter 93 of the Quran) and Surat Alam Nashra (or al Inshira, Chapter 94 of the Quran), and therefore it is not permissible to recite either of them singly. Rather it is indispensable to recite both of them together in succession with separate Bismillah which has come in their midst.

Link: http://www.al-shia.org/html/eng/books/fiqh&usool/islamic-laws/tahrir/17.html

 Salawat!