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My child is taking honors geometry in high school this year and the teacher is starting them off with proofs with is great, however this being their first introduction to proofs it needs to be done right.

The school is using Geometry for Enjoyment and Challenge which I find disturbing in its introduction to theorems and proofs.

The book gives the following for Theorem Procedure:

  1. We present a theorem or theorems.
  2. We prove the theorem(s).
  3. We use the theorems to help prove sample problems.
  4. You are then given the challenge of using the theorems to prove homework problems. Theorems will save you much time if you learn them and use them.

Then it goes right into giving two proofs, followed by six sentences, one of which is

Remember the purpose of a theorem is to shorten your work.

followed by two sample problems and then the set of problems.

The book does not even define definition, hypothesis or conclusion until 17 pages latter.

When my child took algebra we reviewed about twenty books for supplemental reading and my child found A-plus notes for Algebra to be their favorite additional resource, but sadly Rong Yang did not do a book for geometry.

Needless to say as a parent I am striving to do better for my child than this. As such, I searched Amazon and online for books and papers that can introduce a high school student taking geometry to proofs for geometry, and came up with a few items but nothing that hit the nail on the head.

Any references to books or papers either on-line or that can be purchased is welcome. I do ask that any recommendation made were used by a high school student for learning proofs for geometry and that the student found the information useful.

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I come from a bit of Olympiad background so I shall recommend you to look up the books by ArtofProblemSolving.com –  user37450 Sep 8 '12 at 17:06

1 Answer 1

As a high school student, this is the book I will recommend the most:

http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:geometry

The problem with kids is they hate being forced into drill:they need to be motivated to try challenging problems. The website I referred you to is amazing. Firstly, it is used by bright kids from all over the world.I am way past that stage but I think this book will be an awesome resource.

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artofproblemsolving.com/Store/products/intro-geometry/exc1.pdf resembles what you are looking for. –  user37450 Sep 8 '12 at 17:15
    
I wasn't expecting an answer from a high school student but value your answer as equal as or greater than an adult. Glad you took the time to answer. –  Guy Coder Sep 8 '12 at 17:17
    
You are welcome. –  user37450 Sep 8 '12 at 17:19
    
I took a look and some excerpts, the table of contents and the index for the book. I did not see much detail on geometry proofs. Can you give more detail about how this book introduces and teaches proofs? –  Guy Coder Sep 8 '12 at 17:31
1  
Well, the focus of the authors are highly motivated kids and proof-writing.I think asking around the artofproblemsolving.com forum will be better.Though, I feel their curriculum has churned some of the brightest kids in the world. –  user37450 Sep 8 '12 at 17:34

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