I recommend to avoid the "interesting" suggestions of books that include high school geometry but with some advanced insights. These suggestions likely come from the commenters here (many were research mathematicians at least in grad school) versus the needs and enjoyment of high school teachers.
Instead assign a popular, straightforward example text actually used in schools. For simplicity, I would pick one a bit more to the side of old fashioned. This also gives you sort of a base case to compare different ed fads to.
In addition I recommend to assign a text on the different main methods of teaching geometry. If you can't find one, then assign readings on each major "school": articles, etc.
It is not critical to be encyclopedic. Just give them some flavor of a few different approaches (Common Core, traditional, Saxon, etc.) That way when they go teach, wherever they get a job they feel a bit confident that there are several ways of skinning a cat. That there is not one correct school of geometry education (i.e. there is no Euclidean proof of how to teach Euclid). Do NOT feel like you need to be an expert on every school of math ed (too harsh on yourself). Just give them an honest exposure to at least three methods--you will learn something also. [However I would NOT emphasize your own lack of knowledge--students find that a turnoff when the teacher prostrates himself like that...and it reduces confidence.]
A quick Amazon search found this for a math ed text: https://www.amazon.com/Learning-Teaching-Geometry-Secondary-Schools/dp/0415856914#reader_0415856914 I actually like the modeling approach but would prefer it had a bit more of a review of different methods (has some in a historical context) versus just pushing their approach. But take a look at it. And do a Google/Amazon search yourself.
In addition, there is a very active blogosphere of math ed (secondary school edu refomers as well as practitioners). It is NOT a well connected graph (haha) to this MESE community. Below are a few links. You can look through and find others as well. But I think having the students read some blogs will give them excellent insights from real practitioners and also help them understand the whole multi cat skin idea. Also I think they will enjoy that versus just articles and books (less dry). Plus there is the possibility they just play the link game and wander onto other things that interest them on the topic.