Geometry Demystified: A Self-Teaching Guide by Stan Gibilisco

By Stan Gibilisco

Attempt offers a good, and absolutely painless solution to examine the basics and basic techniques of geometry. Self-teaching consultant bargains multiple-choice questions on the finish of every bankruptcy, and a 100-question self-test. Softcover.

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IT’S THE LAW! There are two properties that a four-sided geometric figure absolutely must have—laws it is required to obey—if it is to qualify as a legitimate plane quadrilateral. First, all four vertices must lie in the same plane. Second, all 39 Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use. CHAPTER 3 Quadrilaterals 40 four sides must be straight line segments of finite, positive length. Curves are not allowed, nor are points, infinitely long rays, or infinitely long lines.

Here are some useful facts concerning these four-sided plane figures. SUM OF MEASURES OF INTERIOR ANGLES No matter what the shape of a quadrilateral, as long as all four sides are straight line segments of positive and finite length, and as long as all four vertices lie in the same plane, the sum of the measures of the interior angles is 3608 (2 rad). Figure 3-7 shows an example of an irregular quadrilateral. The interior angles are denoted w, x, y, and z. In this example, angle w measures more than 1808 ( rad).

The vertices of a triangle always lie in a single geometric plane, because any three points, no matter which ones you choose, define a unique geometric plane. But when you have four points, they don’t all necessarily lie in the same plane. ’’ This is why a four-legged stool or table often wobbles, and why it is so difficult to trim the lengths of the legs so the wobbling stops. Once the ends of the legs lie in a single plane, and they define the vertices of a plane quadrilateral, the stool or table won’t wobble, as long as the floor is perfectly flat.

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