Precalculus with Integrated CalculusXYZ Homework Edition

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Chapter 16: Geometry Review

This section serves as a review of the concept of `angle' and the use of the degree system to measure angles. Recall that a ray is usually described as a `half-line' and can be thought of as a line segment in which one of the two endpoints is pushed off infinitely distant from the other, as pictured below. The point from which the ray originates is called the initial point of the ray.

Figure: A ray with initial point .
Figure 16.1 A ray with initial point P .

When two rays share a common initial point they form an angle and the common initial point is called the vertex of the angle. Two examples of what are commonly thought of as angles are

Figure: An angle with vertex .
Figure 16.2 An angle with vertex P .
Figure: An angle with vertex .
Figure 16.3 An angle with vertex Q .

However, the two figures below also depict angles - albeit these are, in some sense, extreme cases. In the first case, the two rays are directly opposite each other forming what is known as a straight angle; in the second, the rays are identical so the `angle' is indistinguishable from the ray itself.

Figure: A straight angle.
Figure 16.4 A straight angle.
Coordinate-plane figure.
Figure 16.5

Adapted from Precalculus, Preliminary 4th Edition (integrated calculus), by Carl Stitz and Jeff Zeager (stitz-zeager.com), licensed under CC BY-NC-SA 3.0. Changes were made: reformatted as an accessible XYZ web edition. License: CC-BY-NC-SA-3.0.

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