Conditions, Pillars (Arkan) & Obligatory (Wajib) Parts of Salah (Prayer) & Pillars (Arkan) & Obligatory (Wajib) Parts of Wudu (Ablution) & Ghusl (Bath):
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Conditions of the Validity of Prayer (Salah):
The conditions of the validity of prayer are 9 in all which are as follows:
(1) Being Muslim.
(2) Being of sound mind.
(3) Discernment.
(4) Being free of ritual impurity.
(5) Removal of tangible impurity.
(6) Covering the ‘awrah.
(7) The time for that prayer should have begun.
(8) Facing the qiblah.
(9) Forming the right intention.
Source: https://islamqa.info/en/answers/107701/conditions-of-the-validity-of-prayer
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Pillars (Arkan) of prayer (Salah):
Rukon means pillar. Arkan is the plural of Rukon. These are the essentials parts of prayer. Leaving it intentionally or by mistake invalidates the prayer. There are 14 pillars of prayer which are as follows:
(1) Standing during obligatory prayers if one is able to do so.
(2) The opening takbeer (saying “Allahu akbar”).
(3) Reciting al-Faatihah.
(4) Rukoo’ (bowing), the least of which means bending so that the hands can touch the knees, but the most complete form means making the back level and the head parallel with it.
(5) Rising from bowing.
(6) Standing up straight.
(7) Sujood (prostration), the most perfect form of which is placing the forehead, nose, palms, knees and toes firmly on the ground, and the least of which is placing a part of each of these on the ground.
(8) Rising from prostration.
(9) Sitting between the two prostrations. However one sits is good enough, but the Sunnah is to sit muftarishan, which means sitting on the left foot and holding the right foot upright with the toes pointing towards the qiblah.
(10) Being at ease in each of these physical pillars.
(11) The final tashahhud.
(12) Sitting to recite the final tashahhud and the two salaams.
(13) The two salaams. This means saying twice, “al-salaamu ‘alaykum wa rahmat-Allah (Peace be upon you and the mercy of Allah).” In naafil prayers it is sufficient to say one salaam; the same also applies to the funeral prayer.
(14) Doing the pillars in the order mentioned here. If a person deliberately prostrates before bowing, for example, the prayer is invalidated; if he does that by mistake, he has to go back and bow, and then prostrate.
Source: https://islamqa.info/en/answers/65847/obligatory-parts-and-sunnah-acts-of-prayer
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Obligatory (Wajib) parts of prayer (Salah):
After Rukon is the place of Wajib, which means obligatory. If any of it is missed intentionally, then the prayer is invalidated and if any of it is missed by mistake, then one must offer ‘Sujud as-Sahw‘. The obligatory parts of prayer are 8 which are as follows:
(1) Takbeers other than the opening takbeer.
(2) Saying “Sami’a Allahu liman hamidah (Allah hears those who praise Him” – for the imam and for the one who is praying alone.
(3) Saying “Rabbana wa laka’l-hamd (Our Lord, to You be praise)”.
(4) Saying “Subhaana rabbiy al-‘azeem (Glory be to my Lord Almighty)” once when bowing.
(5) Saying “Subhaana rabbiy al-a’laa (Glory be to my Lord most High)” once when prostrating.
(6) Saying “Rabb ighfir li (Lord forgive me)” between the two prostrations.
(7) The first tashahhud.
(8) Sitting for the first tashahhud.
Source: https://islamqa.info/en/answers/65847/obligatory-parts-and-sunnah-acts-of-prayer
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Pillars of Wudu (Ablution):
There are 6 essential pillars of wudu which are as follows:
(1) Washing the face, of which the mouth and nose are part.
(2) Washing the arms up to the elbows.
(3) Wiping the head.
(4) Washing the feet up to the ankles.
(5) Washing these parts of the body in the proper order.
(6) Doing these actions consecutively (that is, washing one after the other, with no lengthy lapse of time in between).
Source: https://islamqa.info/en/answers/226422/what-are-the-pillars-of-wudu
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Obligatory Parts of Ghusl (Bath):
There are 4 Obligatory parts of Ghusl (Bath) which are as follows:
(1) Form the intention to purify oneself from impurity: janabah (impurity following sexual discharge), menses or nifas (postpartum bleeding).
(2) Rinsing the mouth.
(3) Rinsing the nose.
(4) Wash the entire body with water once, making sure that the water reaches the roots of the hair and the places that it cannot reach easily, such as the armpits and backs of the knees.
Source: https://islamqa.info/en/answers/82344/how-to-make-ghusl-for-major-impurity