I have been looking for a book that covers the most elementary parts of Geometry, such as similar triangles, circles(arc, sector and others), Pythagorean theorem, Sine and Cosine Laws, so basically a high school Geometry course. I need it to be comprehensive, covering everything in a high school Geometry course, including Coordinate Geometry; it has to cover everything Plane and Solid Geometry.

Although my Geometry is quite weak, I can make huge strides, as I've learnt Algebra and some Calculus via A-Level Maths and Further Maths.

And I'm going to need to cover all the basics of Geometry within two months. I need a book with a lot diagrams, something like Kiselev's Geometry was quite hard for me to comprehend, as I'm mostly a visual learner. Hopefully, the book also has a lot of exercises, too, as the main way of learning is to keep practising problems.

I'm absolutely desperate to become more advanced in my Geometry. So if anyone can help, that would be really, really appreciated.

Thank you all,

And let the recommendations begin.

P.S. I'm going to take the STEP Paper and MAT, so I need something as soon as possible.

  • $\begingroup$ This is a very soft question, and I understand peoples need to downvote this question, but I just need a bit of advice from experience Mathematicians to better myself. $\endgroup$ – user158227 May 19 '15 at 11:46
  • $\begingroup$ Are you doing this just for the exams? $\endgroup$ – Rammus May 19 '15 at 11:52
  • $\begingroup$ I cannot fix the mistake I made when writing everyone. I was meant to write Hi, everyone, but I cannot edit for some reason. Sorry about that. $\endgroup$ – user158227 May 19 '15 at 11:52
  • $\begingroup$ Dear Rammus, this is not just for exams, I actually want to be better at my Geometry, but haven't found the right book to guide me. It would also be good for future reference, too. Any textbooks that come to mind? $\endgroup$ – user158227 May 19 '15 at 11:54
  • $\begingroup$ @user158227 It might be worth mentioning that GCSEs / A-Levels are UK based exams, since this is an international site. $\endgroup$ – martin May 19 '15 at 12:10

There are two books by Stephen Siklos: "Advanced Problems in Core Mathematics" and "Advanced Problems in Mathematics" which are designed for STEP, but they're not necessarily "textbooks".

There's also "Lecture Notes on Mathematical Olympiad Courses For Junior Section" volumes 1 & 2 which are pretty good, concise and with lots of problems to do, but no calculus

  • $\begingroup$ Dear danimal, I know of both. Thanks for the recommendation on MO, but I need something that covers all basics of Geometry in a GCSE/A-Level course. A comprehensive Geometry course. And it needs to be visually appealing, because I have trouble visualising when it's just text. And a lot of exercises of course. I have to be quite advanced at Geometry, so a textbook, study guide or revision book would do. Thanks for the help! $\endgroup$ – user158227 May 19 '15 at 12:04
  • $\begingroup$ I need to be very good at Geometry in order to tackle a question Geometry related in either the STEP or MAT. $\endgroup$ – user158227 May 19 '15 at 12:07
  • $\begingroup$ there is so little real geometry in GCSE/A-level - really it's sine/cosine rules, SOHCAHTOA/Pythagoras, and some radians/circle stuff with little else... $\endgroup$ – danimal May 19 '15 at 12:31
  • $\begingroup$ And that's the real problem with the curriculum - it does not teach Geometry to good level. It's super frustrating, because I know a few textbooks, but I'm looking for something specific. $\endgroup$ – user158227 May 19 '15 at 12:37
  • $\begingroup$ Well if you're preparing either for MAT or STEP you won't need anything that not in the A-level syllabus $\endgroup$ – danimal May 19 '15 at 12:40

This book has the complete syllabus needed for STEP


This is a textbook which explains everything you need and more

and if you need lots more question below is the problem book


This book is aimed at Advanced High school students. Great book and in cheap dover print.

  • $\begingroup$ Dear MRK, bear in mind I'm not fluent with geometry and need a book that could refresh my mind and give me a lot of exercises. $\endgroup$ – user158227 May 20 '15 at 10:29
  • $\begingroup$ @user158227 I have updated my answer to include a textbook for you, i recommend you use textbook first and if you have more time also do problem book which is also listed above. $\endgroup$ – MRK May 20 '15 at 14:00
  • $\begingroup$ Dear MRK, thank you, but isn't it written in the same style as Kiselev's Geometry? I might just stick with Kiselev for now and see how I get on. $\endgroup$ – user158227 May 20 '15 at 18:46

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