Math 7

Unit 8 Geometry

Lesson 8.3  Constructing Perpendicular Bisectors

Focus

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

Use a variety of methods to construct perpendicular bisectors of line segments.

TEXT Page 306

Read/Work through the  Focus  section at the top of page 306 in  your textbook.

This website lets you explore two important properties of a rhombus.

Watch

Video Tutorial

Explore

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

TEXT Page 306

Read/Work through the  Explore  section on Page 306 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.

Perpendicular lines demonstration  (optional)

Video Tutorial

Drag the locators.    (the "cross hair" points)

The blue line will always be perpendicular to the red line.     (and vice versa)

The blue line is actually a special perpendicular line.

The blue line is the perpendicular bisector of the red line   (and vice versa)

The blue line goes through the midpoint (middle) of the red line, and the blue line is perpendicular to the red line.

When you draw a line to divide a line segment into two equal parts, you bisect the segment.

When the bisector is drawn at right angles to the segment, the line is the perpendicular bisector of the segment.

Manipulate[
mid = (p10 + p11)/2;

Graphics[{

(*a line*)

{Thickness[0.005],Red,Line[{p10, p11}]},
{Thin,Green,Line[{p12, p13}]},

If[showit, {Thin,Blue,Line[{mid + (p10 - mid).RotationMatrix[π/2], mid + (p11 - mid).RotationMatrix[π/2]}]}, Black],

If[showit2, {Thin,Purple,Line[{mid +3 (p10 - mid).RotationMatrix[ang], mid + 3(p11 - mid).RotationMatrix[ang]}]}, Black]

},PlotRange->{{-10,10},{-10,10}}, ImageSize->600],

{{p10,{2,2}},{-8,-8},{8,8},Locator},
{{p11,{-2,-2}},{-8,-8},{8,8},Locator}, 
{{showit,False, "Show Perpendicular Bisector"},{True,False}, ControlPlacement->Left},
{{p12,{5,5}},{-8,-8},{8,8},Locator},
{{p13,{5,-5}},{-8,-8},{8,8},Locator},
{{ang, π/3, "Bisector Angle"},0, π, ControlPlacement->Left},
{{showit2,False, "Show Bisector"},{True,False}, ControlPlacement->Left},
SaveDefinitions->True

]

Watch

Video Tutorial

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 midpoint of a line and creating perpendicular lines.
The most important thing to understand is that the perpendicular bisector of a line segment cuts the line segment in half at a 90° angle.

TEXT Pages 306 - 307

Read/Work through the  Connect  section on Pages 306 - 307  in your textbook.

Animation

This website shows the steps used to create a perpendicular bisector of a line segment using a compass and a straight-edge

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 Page 308

Work through the Example  on Page 308 in your textbook.

I covered many of these ideas in the Explore video.

Practice Problems

Many of these questions would be difficult/impossible to make a video for, unless I was doing it “in real life” and I don’t have the technology for that!
The questions are pretty straight-forward and encourage you to simply try the ideas presented in the lesson, using any of the tools you might have access to.
(protractor, ruler, triangle, etc.)

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 2,    I didn’t do a video for this one.
It’s not likely that you would have a Mira,  I don’t!
You could create your perpendicular bisector using any of the methods covered in the lesson.
You would check and make sure that the perpendicular bisector cuts your original line segment exactly in half,  at a 90° angle.

Question 3,    I didn’t do a video for this one.

Question 8,    THIS WEBSITE illustrates the ideas of the question.

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!

({{"Question 1",  ,  , Question 4 , "Question 5"}, {"Question 6", "Question 7", "Question 8", "Question 9", }})