Lesson 51 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 x^{2} or y^{2}.
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 51A.
A parallelogram is a quadrilateral (foursided 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.
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.
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 51, 52, and 53.
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 sameside 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 sameside 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 sameside interior)?
2. What is measurement of angle m ?
3, What type are angle z and angle CAD ( alternate interior or sameside 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 53 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 51B.