Algebraic of properties of Parallelogram

​Algebraic Properties for Parallelograms

In algebra, parallelogram properties help solve for missing sides and angles

Properties for Parallelograms

• Both pairs of opposite sides are parallel.

• Both pairs of opposite sides are congruent

• Both pairs of opposite angles are congruent

• Consecutive angles (Same-Side interior angles) are supplementary

• Diagonals bisect each other

Multiple Choice

Which is NOT a property of a parallelogram?

• Diagonals bisect each other
• Diagonals are congruent
• Both pairs of opposite sides are parallel
• Both pairs of opposite angles are congruent

​Parallelogram Opposite Sides Theorem

Opposite sides are congruent
AB = CD, AD = BC

​then

​then

Fill in the Blanks

Fill in the Blanks

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 7
• 13

• 0
• 4

Fill in the Blanks

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 7
• 22

• 0
• 4

Multiple Choice

All of the angles of a parallelogram and rectangle have a sum of what?

• 90°

• 180°

• 270°

• 360°

Multiple Choice

3 angles of a quadrilateral are 110, 120 and 50.  What is the measure of the 4th angle?

• 60
• 70
• 80
• 130

​Parallelogram Diagonals Theorem

The diagonals of a parallelogram bisect each other
(cut each other in half at their intersection point).

A

B

C

C

C

D

E

​Then

​Then

Multiple Choice

The diagonals of a parallelogram _______ each other.

• bisect

• equal

• are perpendicular to

• complement

Fill in the Blanks

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 14

• 20

• 12

• 17

In the parallelogram ABCD

Triangle ABC and Triangle ADC,

AC = AC (common side)
By ASA congruence criterion, two triangles are congruent to each other.

Alternate interior angles are equal.

∠1 = ∠4

∠2 = ∠3

​​Parallelogram Angles Theorem

​∠1 = 60 then ∠4 =60

∠2 = 10 then ∠3 = 10

Fill in the Blanks

Multiple Choice

Find angle CDE

• 23^o
• 80^o
• 117^o
• 67^o

Independent work

This is a grade

Multiple Choice

Opposite sides of parallelograms are _______ and _______.

• parallel

  and

  congruent

• congruent

  and

  consecutive

• parallel

  and

  perpendicular

• parallel

  and

  supplementary

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 7
• 1
• 5
• 2

Multiple Choice

In a triangle, how many total degrees are there?

• 100%
• 180 degrees
• it varies
• 360 degrees

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 0
• 6
• 5
• 9

Multiple Choice

Find y

• 25^o
• 35^o
• 120^o
• 80^o

Multiple Choice

Find the value of the variable.

• 7

• 11

• 5

• 13

Multiple Choice

What is the measure of ∠U?

• 95°

• 85°

• 75°

• 90°

Multiple Choice

$$m\angle G=$$  

• 132

• 48

• 228

• 66

Multiple Choice

Solve for y.

• 17

• 7

• 2

• 6

Multiple Choice

If ABCD is a parallelogram, what is the length of BD? 

• 10
• 11
• 7
• 5

Fill in the Blanks