asslamungalaikum
Hai...
May name is WH.Khosi
I'm a muslim from the the largest Islamic country in the world (Indonesia), with a Muslim population of 228,608,665 in 2017
with that number we can seize the iron throne (game of throne) hehe ...
please allow me to comment a little, sorry if I make a mistake on my comments
1. Why don't Christians consider Muslims and believe they are children of God?
don't ask me i'm a muslim
2. Don't Muslims worship the God of Abraham from the old testament?
yes
we admit that ibrahim (abraham) is the Rosul (prophet) god
وَاذْكُرْ فِي الْكِتَابِ إِبْرَاهِيمَ إِنَّهُ كَانَ صِدِّيقًا نَبِيًّا Quran Suroh Mariyam :41
"Tell them (Muhammad) the story of Abraham in the Book (Qur'an) is. Verily he is a very righteous man of the Prophet. "
3. Aren't Muslims a part of the old testament?
yes we are
the requirement to be a Muslim is to believe in the holy book before the Koran.
this what quran say :
نَزَّلَ عَلَيْكَ ٱلْكِتَٰبَ بِٱلْحَقِّ مُصَدِّقًا لِّمَا بَيْنَ يَدَيْهِ وَأَنزَلَ ٱلتَّوْرَىٰةَ وَٱلْإِنجِيلَ Quran Suroh. 'Ali `Imran [3] : 3
He sent down the Book (Qur'an) to you in truth; justify the previously revealed book and decrease the Torah and the Gospel,
4. I know they called God Allah but this is the God of the old testament right?
Yes...
from the Quranic verse (Ali Imran; 3) above can be concluded so
but sorry I have not been able to show any specific Quranic verses about it.
let it be my homework.
the and
so thank you
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