| A | P | P | E | N | D | I | X E |
| Geometry and Trigonometry |

E.1

Geometry

|  | Angles

Two angles are equal if

1. | They are vertical angles (see Figure E-1).

| Figure E-1

2. | Their sides are parallel (see Figure E-2).

| Figure E-2

3. | Their sides are mutually perpendicular (see Figure E-3).

| Figure E-3

|  | Triangles

1. | The sum of the angles of any triangle is 180° (see Figure E-4).

| Figure E-4

2. | A right triangle has one angle that is 90°.
3. | An isosceles triangle has two sides that are equal.
4. | An equilateral triangle has three sides that are equal. Each angle of an equilateral triangle is 60°.
5. | Two triangles are similar if two of their angles are equal (see Figure E-5). The corresponding sides of similar triangles are proportional to each other:

| Figure E-5

6. | Two similar triangles are congruent if they can be placed on top of one another to make an exact fit.

|  | Circumferences, Areas, and Volumes of Some Common Shapes

1. | Triangle of base b and altitude h (see Figure E-6):

| Figure E-6

2. | Circle of radius r:

3. | Sphere of radius r:

4. | Right circular cylinder of radius r and height h (see Figure E-7):

| Figure E-7

E.2

Trigonometry

|  | Basic Trigonometric Functions

1. | For a right triangle, the sine, cosine, and tangent of an angle are defined as follows (see Figure E-8):

| Figure E-8

2. | The secant , cosecant , and cotangent of an angle are defined as follows:

|  | Triangles and Trigonometry

1. | The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides (see Figure E-8):

2. | The law of cosines and the law of sines apply to any triangle, not just a right triangle, and they relate the angles and the lengths of the sides (see Figure E-9):

| Figure E-9

|  | Other Trigonometric Identities

1. |
2. |
3. |
4. |
5. |
6. | If , If ,
7. | If , If

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.