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William, the sight you referenced for the Pt111 will fit with no problem on your AR. You would just need this riser to raise the sight to the correct level : https://www.budsgunshop.com/catalog/product_info.php/products_id/88146/Aimshot+MT61172+Quick+Release+Riser+Base+For+AR+AR-15+Style+ --- The Taurus PT111 is not setup to add a red dot sight unfortunately. There are several available lasers for the PT111 though here : https://www.amazon.com/s/?ie=UTF8&keywords=taurus+pt111+g2+laser&tag=googhydr-20&index=aps&hvadid=178116451122&hvpos=1t1&hvnetw=g&hvrand=3301746547504105827&hvpone=&hvptwo=&hvqmt=b&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=1021278&hvtargid=kwd-84246049477&ref=pd_sl_3b7ytakvjc_b

almost any red dot will work on the AR you may need a riser. there are lots of lasers that will fit the under barrel rail of your Taurus putting a red dot on is almost impossible most defense handguns are not set up for optical sights but some companies are coming out with guns that are optics ready like the glock mos https://www.budsgunshop.com/catalog/product_info.php/products_id/50343/Glock+G34+G5+9MM+17%2B1+5.3%5C%5C%5C+MOS+AS