Basic Trigonometric Figures - dummies

By Mary Jane Sterling

Segments, rays, and lines are some of the basic forms found in geometry, and they’re almost as important in trigonometry. You use those segments, rays, and lines to form angles.

Drawing segments, rays, and lines

A segment is a straight figure drawn between two endpoints. You usually name it by its endpoints, which you indicate by capital letters. Sometimes, a single letter names a segment. For example, in a triangle, a lowercase letter may refer to a segment opposite the angle labeled with the corresponding uppercase letter.

A ray is another straight figure that has an endpoint on one end, and then it just keeps going forever in some specified direction. You name rays by their endpoint first and then by any other point that lies on the ray.

A line is a straight figure that goes forever and ever in either direction. You only need two points to determine a particular line — and only one line can go through both of those points. You can name a line by any two points that lie on it.

The figure shows a segment, ray, and line and the different ways you can name them using points.


Intersecting lines

When two lines intersect — if they do intersect — they can only do so at one point. They can’t double back and cross one another again. And some curious things happen when two lines intersect. The angles that form between those two lines are related to one another.

Any two angles that are next to one another and share a side are called adjacent angles. Here, you see several sets of intersecting lines and marked angles. The top two figures indicate two pairs of adjacent angles.


Can you spot the other two pairs? The angles that are opposite one another when two lines intersect also have a special name. Mathematicians call these angles vertical angles. They don’t have a side in common. You can find two pairs of vertical angles here; the two middle figures indicate the only pairs of vertical angles. Vertical angles are always equal in measure.

Why are these different angles so special? They’re different because of how they interact with one another. The adjacent angles here are called supplementary angles. The sides that they don’t share form a straight line, which has a measure of 180 degrees. The bottom two figures show supplementary angles. Note that these are also adjacent.