Math 7

Unit 8 Geometry

Lesson 8.4  Constructing Angle Bisectors

Focus

The FOCUS section introduces the main concept that will be covered in the lesson.

Use a variety of methods to construct bisectors of angles.

There isn’t a Focus activity in this lesson.

TEXT Page 310

Read/Work through the  Focus  section at the top of page 310 in  your textbook.

Explore

Explore an idea or problem.
The exploration provides the background for the ideas presented in the lesson.

TEXT Page 310

Read/Work through the  Explore  section on Page 310 in your textbook.

You can do this activity on your own.
Do your best to answer the questions, then watch the Video Tutorial for help or to check your answers.

You can create your own “piece of pie” to divide,  or, if you like, download and print THIS FILE to use.

There are many possible methods you could use here,  I will cover them in the Connect part of the lesson.

Connect

Connect summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

Depending on the tools you have available,  you have options for finding the bisector of an angle.
The most important thing to understand is that the bisector of an angle divides the angle into two parts (two angles of equal measure)

TEXT Pages 310 - 311

Read/Work through the  Connect  section on Pages 310 - 311  in your textbook.

I’ve provided links (below) to help present the ideas of the lesson.

Getting the same information in multiple ways can help with understanding.

Angle Bisector Interactive  Constructions

Step  by step with circles
LINK

Another example, this is the same as the above example, but “cleaner” since it uses arcs instead of entire circles.
LINK

Another example, this one uses the same technique,  but you can run it one step at a time.
LINK

Angle bisector illustrated

This isn’t a construction, it illustrates the IDEA of an angle bisector.
LINK

Use a protractor and a ruler

Here is the method in one diagram.  
I hope you can follow the needed steps to get to here.

•	Draw an angle
•	Place your protractor at the vertex of the angle
•	Measure the angle  (in this case,  it's 54° or very close to it)
•	Divide that number by 2,  so 54 ÷ 2 = 27
•	It's not shown in the diagram, but you would put a mark at 27 degrees, then move the protractor and use a ruler to draw the bisector.

Example

The Example will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example

TEXT Pages 311 - 312

Work through the Example on Pages 311 - 312  in your textbook.

Watch

Video Tutorial

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Assessment Focus a question that gives a good example of the kind of question you would be expected to answer after completing the lesson

Take It Further questions offer enrichment and extension.

Notes

Question 1,    I didn’t do a video for this one.

Question 5,    I didn’t do a video for this one.
A ruler and compass will be a lot more accurate than Mira or paper folding.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

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