Geometry Essentials For Dummies

Mark Ryan

• Editore: For Dummies
• Anno: 2019
• ISBN:
  9781119590460
• Edizione: 1
• Argomento: Mathematik
• Categoria: Algebraische Geometrie

Geometry Essentials For Dummies (9781119590446) was previously published as Geometry Essentials For Dummies (9781118068755). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

Just the critical concepts you need to score high in geometry

This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams.

• Get down to the basics — get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals
• Conquer proofs with confidence — follow easy-to-grasp instructions for understanding the components of a formal geometry proof
• Take triangles in strides — learn how to take in a triangle's sides, analyze its angles, work through an SAS proof, and apply the Pythagorean Theorem
• Polish up on polygons — get the lowdown on quadrilaterals and other polygons: their angles, areas, properties, perimeters, and much more

Chapter 1

An Overview of Geometry

IN THIS CHAPTER

Surveying the geometric landscape: Shapes and proofs

Understanding points, lines, rays, segments, angles, and planes

Cutting segments and angles in two or three congruent pieces

Studying geometry is sort of a Dr. Jekyll-and-Mr. Hyde thing. You have the ordinary geometry of shapes (the Dr. Jekyll part) and the strange world of geometry proofs (the Mr. Hyde part).

Every day, you see various shapes all around you (triangles, rectangles, boxes, circles, balls, and so on), and you’re probably already familiar with some of their properties: area, perimeter, and volume, for example. In this book, you discover much more about these basic properties and then explore more advanced geometric ideas about shapes.

Geometry proofs are an entirely different sort of animal. They involve shapes, but instead of doing something straightforward like calculating the area of a shape, you have to come up with a mathematical argument that proves something about a shape. This process requires not only mathematical skills but verbal skills and logical deduction skills as well, and for this reason, proofs trip up many, many students. If you’re one of these people and have already started singing the geometry-proof blues, you might even describe proofs — like Mr. Hyde — as monstrous. But I’m confident that, with the help of this book, you’ll have no trouble taming them.

The Geometry of Shapes

Have you ever reflected on the fact that you’re literally surrounded by shapes? Look around. The rays of the sun are — what else? — rays. The book in your hands has a shape, every table and chair has a shape, every wall has an area, and every container has a shape and a volume; most picture frames are rectangles, DVDs are circles, soup cans are cylinders, and so on.

One-dimensional shapes

There aren’t many shapes you can make if you’re limited to one dimension. You’ve got your lines, your segments, and your rays. That’s about it. On to something more interesting.

Two-dimensional shapes

As you probably know, two-dimensional shapes are flat things like triangles, circles, squares, rectangles, and pentagons. The two most common characteristics you study about 2-D shapes are their area and perimeter. I devote many chapters in this book to triangles and quadrilaterals (shapes with four sides); I give less space to shapes that have more sides, like pentagons and hexagons. Then there are the shapes with curved sides: The only curved 2-D shape I discuss is the circle.

Three-dimen...