Properities of Parallelograms

Properities of Parallelograms

Do Now:

Review of naming angles and quadrilaterals

Multiple Choice

Name the angle form by lines DE and EF in the long form.

• ∠e

• ∠f

• ∠FED

• ∠FDE

Multiple Choice

Choose the correct name for the angle marked $\angle5.$ 

•  $\angle V$  

•  $\angle JVK$  

•  $\angle IJK$  

•  $\angle IVJ$  

Multiple Choice

Name that shape.

• quadrilateral, rectangle

• quadrilateral, rectangle, square

• quadrilateral, parallelogram, rectangle

• quadrilateral, parallelogram, rectangle, square

Objective: Discover the properites of quadrilaterals.

Today we will be using this presentation for our lesson. What you don't finish in class will be homework.

Multiple Choice

What is the definition of a quadrilateral? Choose the definition that is the most accurate.

• A 4 sided figure where all the angle measure add to 360 degrees

• A rectangle or a square

• any figure- it could even be a circle.

Multiple Choice

What is the definition of a parallogram? Choose the most accurate answer.

• any 4 sided figure where the angles measures add to 360 degrees

• A 4 sided figure where a the oppposite sides are parallel and all the angles add to 360 degrees.

• a 4 sided figure where the 4 angles are all right angles

• Any figure- it could even be a circle.

Multiple Choice

What is the definition of a rectangle? Choose the definitions that is hte most accurate.

• any 4 sided figures where the angles measures add to 360 degrees

• any 4 sided figure where all 4 angles are right angles.

• Any 4 sided figure where all 4 angles are right angles and all the sides are equal.

• Any figure, it could even be a circle.

Multiple Choice

What is the definition of square? Choose the answer that is the most accurate.

• Any 4 sided figure where the angle measures add to 360 degrees.

• any 4 sided figure with 2 sets of parallel lines

• Any 4 sided figure where 4 right angles and all the sides are congruent.

• Any figure, it could even be a circle.

Draw the following diagram in your notes. You will need it to answer the following questions.

Keep track of your answers on in your notebook as well as in this presentation. It will help you answer the questions.

Multiple Choice

What is the slope of line segment AD and line segment CB?

•  $\ \frac{3}{2\ }\ and\ \frac{2}{3}$  

•  $\frac{2}{3}\ and\ \frac{2}{3}$  

•  $\frac{3}{2\ }\ and\ \frac{3}{2\ }$  

Multiple Choice

Point E is __________________ of AC and BC. Chose the most accurate answer.

• the midpoint

• a point on the line.

• the intersection point

Definitions of Bisect: Cuts in half.

• Lines segment AC is bisected by point E and line segment DB.

Find the missing angles.

Be sure to use your toolbox!

Multiple Choice

Find the

 $m\angle AEB$  

• 51 degrees

• 90 degrees

• 20 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle DEC$  

• 51 degrees

• 90 degrees

• 20 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle ECD$  

• 51 degrees

• 90 degrees

• 20 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle EBC$  

• 51 degrees

• 90 degrees

• 20 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle EDC$  

• 51 degrees

• 90 degrees

• 20 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle EAB$  

• 51 degrees

• 90 degrees

• 20 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle EBA$  

• 51 degrees

• 90 degrees

• 20 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle AED$  

• 51 degrees

• 90 degrees

• 129 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle BEC$  

• 51 degrees

• 90 degrees

• 129 degrees

• 59 degrees

• 39 degrees

Multiple Choice

Find the

 $m\angle ECB$  

• 51 degrees

• 90 degrees

• 129 degrees

• 59 degrees

• 31 degrees

Multiple Choice

Find the

 $m\angle EAD$  

• 51 degrees

• 90 degrees

• 129 degrees

• 39 degrees

• 31 degrees

Multiple Choice

Find the

 $m\angle ADE$  

• 51 degrees

• 90 degrees

• 129 degrees

• 39 degrees

• 20 degrees

Multiple Choice

Find the

 $m\angle BAD$  

• 51 degrees

• 90 degrees

• 121 degrees

• 39 degrees

• 31 degrees

Multiple Choice

Find the

 $m\angle DCB$  

• 51 degrees

• 90 degrees

• 121 degrees

• 39 degrees

• 31 degrees

Multiple Choice

Find the

 $m\angle ADC$  

• 59 degrees

• 90 degrees

• 121 degrees

• 39 degrees

• 31 degrees

Multiple Choice

Find the

 $m\angle ABC$  

• 59 degrees

• 90 degrees

• 121 degrees

• 39 degrees

• 31 degrees

Multiple Choice

The following angles are ____________ each other.

 $\angle BAD\ and\ \angle DCB\$  

• opposite from 

• adjacent (next to)

Multiple Choice

 $m\angle BAD\ +\ m\angle DCB\ +m\angle ADC\ +\ m\angle ABC\ =\$  

• 90 degrees

• 360 degrees

Open Ended

 $\overline{AC}\ and\ \overline{BD}\$  are called diagonals.  Write a possible definition of a diagonal.

Multiple Choice

Diagonals of a parallelogram intersect at ____________________.

• the midpoint, which is exactly in the middle of both diagonals.

• any point they want.

Multiple Choice

 $m\angle DAB\ +\ m\angle ABC\ =\$  

• 180 degrees

• 360 degrees.

Multiple Choice

 $m\angle DAB\ and\ m\angle ABC\ are$  

• opposite

• Adjacent (next to)

Add the following slide to your notes:

Test yourself

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 4
• 12
• 5
• 2

Multiple Choice

Find x.

• 82
• 92
• 98
• 102

Multiple Choice

Find x.

• 75
• 85
• 105
• 95

Multiple Choice

Find the m∠SRQ.

• 40°

• 140°

• 50°

• 180°

Multiple Choice

The opposite angles of a parallelogram are ...

• complementary
• congruent
• supplementary
• perpendicular

Multiple Choice

What do we know about the diagonals of ALL parallelogram?

• They are congruent
• They bisect each other
• They are perpendicular to each other
• They are parallel to each other

Multiple Choice

In the picture, side AB must be congruent to which side?

• AE
• AD
• CD
• BC

Multiple Choice

In the picture, side BE must be congruent to ______ if BC is parallel to AD and AB is parallel to CD.

• AE

• ED

• CD

• BD