1. Module 5

1.14. Page 4

Mathematics 10-3 Module 5 Lesson 1

Module 5: Angles

 

Bringing Ideas Together

 

In Getting Started and Explore, you examined what it means to bisect an angle. In your next activity you will construct the bisector of an angle using a classical approach—one that geometers have used for thousands of years.

 

You will use only your compasses and a straightedge. After you are done, you will use your protractor to check the accuracy of your construction.

 

View “Bisect an Angle,” which shows the technique of using a compass to bisect an angle. This is “Example Two” on the applet.

 

Self-Check

 

Respond to these questions. When you are finished, check your answers.

 

SC 1. Draw any obtuse angle. Use your compasses and a straightedge to bisect the angle. Check the accuracy of your construction with your protractor.

 

SC 2. A student bisected a 234° angle. A protractor was used to measure each half. The student said that each half was 63°. What mistake might have been made? How large should each half have been?

 

Compare your answers.

 

Using a Carpenter’s Square to Bisect an Angle

 

This photo shows a carpenter’s square placed on a board.

© Tom Oliveira/shutterstock

A carpenter’s square is shown in this photograph.

In construction, carpenters use carpenter squares to bisect angles. You can use one of the squares from your geometry set to bisect an angle. The following example will show the technique of bisecting an angle using a square.

 

Example 1

 

Use a square to bisect an angle.

 

Solution

 

Watch “Lesson 3: Example 1 Solution” to see how to bisect an angle.

 

Self-Check

 

Respond to this question. When you are finished, check your answer.

 

SC 3. Use the method shown in the example to bisect a 120° angle.

 

Compare your answer.

 

Mastering Concepts

 

Try this question. When you are finished, check your answer.

 

Zander says he can bisect a 300° angle by bisecting the 60° angle that completes the full rotation and extends the bisector of the 60° angle in both directions. Is Zander right or wrong?

 

If Zander is right, explain why he is right. If Zander is wrong, explain why he is wrong.

 

Compare your answer.