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Monday, May 27, 2019

501 Geometry Questions (2nd Edition)

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Geometry is the study of figures in space. As you study geometry, you will measure these figures and determine how they relate to each other and the space they are in. To work with geometry you must understand the difference between representations on the page and the figures they symbolize. What you see is not always what is there. In space, lines define a square; on the page, four distinct black marks define a square. What is the difference? On the page, lines are visible. In space, lines are invisible because lines do not occupy space, in and of themselves. Let this be your first lesson in geometry: appearances may deceive.

Sadly, for those of you who love the challenge of proving the validity of geometric postulates and theorems—the statements that define the rules of geometry—this book is not for you. It will not address geometric proofs or zigzag through tricky logic problems, but it will focus on the practical application of geometry towards solving planar (two-dimensional) spatial puzzles. As you use this book, you will work under the assumption that every definition, every postulate, and every theorem is “infallibly” true.

1. The Basic Building Blocks of Geometry
2. Types of Angles
3. Working with Lines
4. Measuring Angles
5. Pairs of Angles
6. Types of Triangles
7. Congruent Triangles
8. Ratio, Proportion, and Similarity
9. Triangles and the Pythagorean Theorem
10. Properties of Polygons
11. Quadrilaterals
12. Perimeter of Polygons
13. Area of Polygons
14. Surface Area of Prisms
15. Volume of Prisms and Pyramids
16. Introduction to Circles and Arcs
17. Circumference and Area of Circles
18. Working with Cylinders, Cones, and Spheres
19. Coordinate Geometry
20. The Slope of a Line
21. The Equation of a Line
22. Transformations, Reflections, Translations, and Rotations

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