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Lesson5-1 old

Page history last edited by Math in a Box - Susan Johnsey gm 4 years, 11 months ago

Lesson 5-1             Properties of Parallelograms

 

Before we begin this lesson there are some important algebra skills that you need to review or learn.

See page 163. There are two methods of solving these algebra equations. You must know both.

You should have studied this in Algebra 1.   You must know these problems. Practice, Practice.

These equations all have a squared variable such as x2 or y2.

 

Here is a special link to some of my examples.   Write them into your notes and place sticky note on them.  

Practice, Practice.

We will use these at other times in the Geometry Course.  Quick Algebra Review ( one variable)

 

First method is factoring.  

The factoring method really has more examples that are not given here. Do you recall factoring? If not let me know.

 

Second method: 

The quadratic formula can also be used to solve these equations. 

All of the equations can be solved with the quadratic formula. Only some of them can be done with factoring.

 

If you need help let me know and I will find some videos for you to watch.    We will use these skills in other Lessons of this book and in other math courses too.

 

 After you work the examples   and the odd numbered problems 1 to 17 page 163 then

 

Complete Assignment 5-1A.  

 

A parallelogram is a  quadrilateral (four-sided figure)

     with both pairs of opposite sides parallel. 

This is the DEFINITION.   

 

In the video below side AB is parallel to side CD and side AD is parallel to side BC.   

Do you recall theorems about parallel lines from chapter 3?

The video is short and quick so please pause it and take a few notes.    Please ignore the advertising in it or click the X on it.

 

Click here for the Video to watch.

 

 

Now let us have a bit of fun experimenting.

 

You can start over if you mess it up!!  Just refresh or reload the page.  YOu must have JAVA on your computer.  Ask an Adult to help you, although your computer probably already has JAVA. Here is the link for information about JAVA.   If you have trouble or do not see anything below then reload (refresh) the page.

 

1.  I drew  quadrilateral ABCD  then

2.  I found the midpoint of each of its sides and

3.  connected those to create EFGH.  

But something surprising happened.   EFGH is not just any 4 sided figure.

 

 

Creating a parallelogram

 

SCROLL up so you can see the WHOLE activity window before you move any of the points and use a full screen.

 

Move the points A or B or C or D and watch the quadrilateral EFGH. What do you notice about the opposite sides EF and GH? Can you move A or B or C or D so that EF and GH are not congruent? Right Click EH -choose OBJECT properties: check "Show Label" and select beside it "Value"; then Close.  Do you see its length now? do same for FG.

 

Sorry, the Geogebra Applet could not be started. Please make sure that Java 1.4.2 or later is installed and active in your browser. (Click here to install Java now

 

LOOK at the diagonals, the pink and green segments. CAN you move the points A or B or C or D so the diagonals are congruent? What do you notice about the angles when the diagonals are congruent? Right click the pink diagonal and choose OBJECT properties: check "Show Label" and select beside it "Value"; then Close. Do you see its length now? do same for green diagonal.

 

Susan Johnsey,    Created with GeoGebra

 

 

In your Geometry Collection add the definition of Parallelogram

       and Theorems 5-1, 5-2, and 5-3.

 

You MUST include the diagrams too. I would add the little red markings too.

Recall how we mark the sides when they are congruent, see page 148 .

 

DO YOU see the red arrows???Those indicate the lines are parallel.

 


 

 

Look for alternate interior angles and same-side interior angles.

 

Remember when we have parallel lines that there are 3 lines to trace to see the angles that are helpful.

Which angles are those?    alternate interior: they make a Z or N shape

and also same-side interior angles: they make a |_|   shape, but you can turn it different ways of course.

 

 

BEFORE you Answer the questions in the Blue area above you must find the measure of angles m and z !!

   1.  What type are angle m and angle CBD ( alternate interior or same-side interior)?  

   2. What is measurement of angle m ? 

   3,  What type are angle z and angle CAD ( alternate interior or same-side interior)?   

   4. What is measurement of angle z ?

  DID you do that?

Answer the questions in the Blue area above and send me an email. HERE: Susan Johnsey

Be sure to state each letter with its measurement and the answers about the theorems.

 

Theorem 5-3 does NOT state that the diagonals are congruent.

 

Look at the diagonals QS and TR. TR is shorter, right???

 

BY  definition of BISECT,   what segments are congruent???

 

Can you mark them with the single red marks

        and then the double red marks??

 

M is the midpoint.

 

LOOK at the angles of 2 parallelograms  (without the diagonals).

Complete Assignment 5-1B.