# Math 152 - Chapter 10 - Dynamic Worksheet

## Part A: Linear Angles

## #1

Using the __ location__ of the two angles to write a definition for a linear angle pair.

## #2

What do you observe about the angle measures of the linear angles?

## #3

Make a conjecture about the sum of the measures of __ any__ linear angle pair.

## Part B: Vertical Angles

## #4

Based on the __ location__ of one of the vertical angle pairs above, write a definition for a vertical angle pair.

## #5

Use points A, B, C, and D to change the angle values. Make a conjecture about the angle measures of a pair of vertical angles.

## Part C: Additional Angle Pairs

**Move the slider to the left so that it reads "Corresponding Angles."**The color-coded angle pairs below are made when a

**transversal**crosses two lines. These particular angle pairs are called

**corresponding angles.**

## #6

Move one of the lines by dragging one of the points on the line. Notice that the pairs stay the same (the colors don’t change). When do the angle pairs seem the most equal in size?

## #7

Now, use the slider at the top of the screen to highlight some __ different__ angle pairs. (Not corresponding angles, but different angle pairs.) Define these pairs based on their location with respect to the transversal.

- Alternate Interior Angles
- Alternate Exterior Angles
- Same Side Interior Angles
- Same Side Exterior Angles

## Part D: The Parallel Postulate

*AB*and

*FC*are

**parallel**. Line

*BC*is called a

**transversal**of lines

*AB*and

*FC*because it transverses (crosses) the lines. Move the lines

*AB*and FC by moving points

*A*,

*B*, or

*C*. Notice as you do, that the lines

*AB*and

*FC*

**. Answer the following questions.**

__remain parallel__## #8

What are the colored angled pairs called?

## #9

What do you notice about the angle measures of the angle pairs?

## #10

Fill in the blanks below to define the Parallel Postulate:
**
Parallel Postulate:** When two ________________________ lines are cut by a _________________________________ , the resulting __________________________________ angles are ______________________.

## #11

Use the Parallel Postulate to **prove **that if two parallel lines are cut by a transversal, then the alternate interior angles are __congruent__. (That is, c=f in the diagram above.)

## #12

Use the Parallel Postulate to **prove **that if two parallel lines are cut by a transversal, then same side interior angles are __supplementary__. (That is, c+e = 180 in the figure above.)