Fundamentals of Math

Fundamentals of Mathematics

Chapter 5: Geometry In this chapter, we will be studying Plane Geometry . A plane is considered to be a flat sheet with no thickness and goes on forever in both directions (think of a large piece of paper that never ends). We seek to study the 2-D figures (circles, triangles, squares, rectangles, etc.) that exist on a plane - we study their properties, relationships, and constructions. So, let us start by defining a few of the basics - lines and angles.

Lines are lengths with no widths and named by their endpoints. List the two endpoints of the line and draw a "line" above them.

This is line ̅̅̅̅ or ̅̅̅̅ ; notice it does not matter which direction you go to name the line. However, most people name the line in the direction they want the reader to follow. For instance, if you want your reader to read the line left to right, you are better off calling the line ̅̅̅̅ as opposed to ̅̅̅̅ .

When two straight lines meet at a common endpoint, an angle is formed (the space between the lines). We call the place where the lines meet the vertex of the angle.

Angles are named using three letters, endpoint 1 - vertex - endpoint 2 . Similar to the line, it doesn't matter which endpoint you deem endpoint 1 or endpoint 2, so in the example, above we could call that ∠ or ∠ ( ∠ is the symbol for angle ), and both refer to the same angle.

We use rulers to help us measure the length of a line, but we use protractors to helps us find the measurements of angles. We then classify angles into four categories based on their size. (1) Angles that measure less than 90° are acute angles. (2) Angles that measure exactly 90° are right angles . (3) Angles that measure more than 90° , but less than 180° are obtuse angles , and lastly, (4) angles that measure exactly 180° are considered straight angles .

Acute Angles

Right Angles

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