Angles in a parallelogram-Geometry Help-MooMooMath

Hi welcome to MooMooMath Today we are going to look at angles in a parallelogram
First we need to know, “ what is a parallelogram?”
A parallelogram is Quadrilateral meaning a polygon with four sides with the opposite sides parallel. We have the top parallel to the bottom (BC is parallel to AD) and (AB is parallel to DC)
This is one property that defines a parallelogram. Another property of a parallelogram is that opposite angles are congruent to each other.
Angle B will be the same measure as angle D
Let's give the angle B a measure equal to 120 degrees. Because angle D is opposite angle B it will also have an angle measure of 120 degrees. Now A and C are congruent ,but they have to have a relationship to D and B and the relationship is that these two consecutive angles are supplementary ,which means they add to 180 degrees. If angle D is 120 degrees then angle A has to be 60 degrees and angle C has to be 60 degrees. Any pair of consecutive angles of a parallelogram are supplementary.
Also, the opposite angles are congruent. Let's try a practice problem. Let's change these numbers and angle C will equal to 80 degrees. We can figure out the other three angles. What do we know about angle A ? Angle A would have to be 80 degrees and angles D and B will have to be supplementary angles to 80, so each angle would be 100 degrees. Remember, opposite angles of a parallelogram are congruent, and adjacent angles are supplementary. Hope this video was helpful on angles of a parallelogram.

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How to find the Area of a Parallelogram

How to find the Area of a Parallelogram

Video How to find the Area of a Parallelogram

 

The formula for finding the area of a parallelogram equals base times height or A=b*h

Please note, the height is not the length of a side but is the distance from base to base. Please see the drawing below.

 

 

 

 

 Problem 1. What is the area of a parallelogram with a base of 8 units and sides of 5 units and a height of 4 units? 

 

 Step 1. Multiply the base of 8 units times the height of 4 units.

 Step 2. 8*4 = 32 units squared

 

Problem 2. What is the area of a parallelogram that has a side of 6 units, a base of 10 units and an angle measure of 60 degrees?

 

 

 

 Step 1. Find the altitude. If you draw a vertex straight down it creates a triangle. See picture below. The triangle is a 30-60-90 triangle. I can use the 30-60-90 rules to find the height of the parallelogram.

The rules of a 30-60-90 are as follows:

 Short leg =x 

Long leg =  x√3

Hypotenuse = 2x

 

 

 

Step 2. The length of the side leg equals 6 and is my hypotenuse in my triangle   

Therefore, 6 =2x so x =3

 Step 3. Now that I know x I can find the height by finding the length of the long leg 

long leg=3√3 

 Step 4. Use area equals base * height  or A =b*h

            10 * 3√3 = 30√3 units^2

 

Top Ten Properties of a Parallelogram

Top Ten Properties of a Parallelogram

1. A parallelogram is a quadrilateral.

2. The opposite sides of a parallelogram are parallel.

3. The opposite angles of a parallelogram are congruent.

4. The opposite sides of a parallelogram are congruent.

5. The perimeter of a parallelogram equals 2 (base + side)

6. The area of a parallelogram equals base * height

7. The adjacent angles of a parallelogram are supplemental.

8. The diagonals of a parallelogram bisect each other. (In other words the cut each other exactly in half.

9. A parallelogram has four sides

10. The sides of a parallelogram must be straight.

Video Parallelogram

Video Area of a Parallelogram

Video Perimeter of a Parallelogram