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Good Day I am looking for a Book that contains detailed proofs of theorems in the field of Euclidean Geometry that are used to solve exams and school work of high school students.

theorems like:

inscribed angle theorem: angle inscribed in a circle is half of the central angle;

Circumscribed circle theorems;

incircle theorems;

stuff like that.

any suggestions?

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3 Answers 3

"Geometry for Enjoyment and Challenge" by Rhoad, Milauskas, and Whipple (published by McDougal-Littell) is a fairly common proof-based high school honors geometry textbook, at least in the greater Chicago metropolitan area.

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Thank you for the reference, i will check that book. actually a solution manual exists either: Solution Manual : Geometry for Enjoyment and Challenge Main Author: Bogan, Kathleen Other Authors: Gilleran, Lori, Wienert, HeidiBogan, Kathleen –  Eliy Arlev Jan 31 '12 at 22:41

I am reminded of a blue book by C.G.Gibson entitled " Elementary Euclidean Geometry-An Undergraduate Introduction". The same author has other books in the series.

One of the main advantages of this book is a well-paced thorough treatment of geometry through Linear Algebra. A careful reader will find many treasures to unearth; a link between linear algebra and geometry will become quite 'evident'!

Let the votes decide how effective has the book been in achieving its goal!

Note:

It has been published by Cambridge University Press---(174 pages)

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It might be worth looking at Kisilev's Geometry, which is pitched at the high school level, and covers the material you're asking about. It has almost 600 exercises (but no solutions).

The first volume deals only with plane Euclidian geometry; there's a second volume covering solid geometry, which introduces Hilbert's axioms, vector spaces, and non-Euclidian geometry.

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+1 for the recommendation of Alexander Givental's baby. One of the world's great classic textbooks. –  Mathemagician1234 Jan 26 '12 at 19:42

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