Books about 2D and 3D figures with explanations and problems?

  • Context: Geometry 
  • Thread starter Thread starter songoku
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SUMMARY

This discussion focuses on recommended books for understanding 2D and 3D geometric figures, specifically addressing concepts such as the Exterior Angle Bisector Theorem, distance calculations in geometric shapes, and properties of regular tetrahedrons. Participants suggest Kiselev's geometry books and resources from the Art of Problem Solving, including "Introduction to Geometry" and "Euclidean Geometry in Mathematical Olympiads" by Evan Chen, as suitable for high school-level students. The conversation emphasizes the importance of proof-heavy texts for deeper comprehension.

PREREQUISITES
  • Understanding of basic geometric principles and theorems
  • Familiarity with 2D and 3D shapes, including triangles and tetrahedrons
  • Knowledge of distance formulas in geometry
  • Ability to interpret and construct geometric proofs
NEXT STEPS
  • Explore Kiselev's geometry books for foundational concepts
  • Study "Introduction to Geometry" by the Art of Problem Solving for problem-solving techniques
  • Investigate "Euclidean Geometry in Mathematical Olympiads" by Evan Chen for advanced problem sets
  • Practice geometric proofs related to the Exterior Angle Bisector Theorem
USEFUL FOR

High school students, educators in mathematics, and anyone interested in enhancing their understanding of geometric concepts and problem-solving strategies.

songoku
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I am looking for books that contain explanations (or to be able to answer) about something like this:

1) Exterior Angle Bisector Theorem
The external angle bisector of a triangle divides the opposite side externally in the ratio of the sides containing the angle. This condition occurs usually in non-equilateral triangles.

2) Given cube ABCDEFGH with side 2 units and line DF passes through plane ABGH at point T. Find distance ET

3) Given regular tetrahedron TABC with side 3 cm. M is mid point of AT and N is mid point of BC. Find length of MNAny books are ok but preferably high school level.

Thank you
 
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Is a proof-heavy text okay?
 
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Muu9 said:
Is a proof-heavy text okay?
no problem
 
Try the two geometry books by Kiselev, or the Art of Problem Solving Introduction to Geometry or Euclidean Geometry in Mathematical Olympiads by Evan Chen
 
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Thank you very much Muu9
 

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