# Polygons

### Caroline Hebert, 7th hour

## Different Quadrilaterals

## Parallelograms

## How to solve a parallelogram

## 1. Solve for X and Y You have to solve for X and Y to find what the angles equal. | ## 2. Identify what you already know by looking at the parallelogram in the problem.1. You know that 6x=18 because they are alternate interior angles. 2. You know that 3y+4=5y+2 because diagonals bisect each other. | ## 3. Solve for X 1. Isolate your variable (X) 2. To isolate your variable, you have to divide 18 by 6 3. 18 divided by 6 is 3 4. Your answer is X=3 |

## 2. Identify what you already know by looking at the parallelogram in the problem.

1. You know that 6x=18 because they are alternate interior angles.

2. You know that 3y+4=5y+2 because diagonals bisect each other.

## 4. Solve for Y 1. Combine like terms....By subtracting 3y from 5y 2. Combine like terms...By subtracting 2 from 4 3. Isolate your variable...By divide 2y by 2 4. Your answer is Y=1 | ## Your answer... X=3 Y=1 | ## Check your answer Plug in your variables and solve. If your answers for corresponding angles equal each other, then you are correct. |

## 4. Solve for Y

2. Combine like terms...By subtracting 2 from 4

3. Isolate your variable...By divide 2y by 2

4. Your answer is Y=1

## Properties of Parallelograms

## Real life examples of an isosceles trapezoid....

## The Window This window is an isosceles trapezoid because it has a line of symmetry bisecting it into one pair of opposite sides. | ## Popcorn COntainer This popcorn container is an isosceles trapezoid because it is a quadrilateral with a line of symmetry bisecting it straight down the middle. |

## Real life examples of a trapezoid...

## The Box Garden The wooden box in which the garden is grown is a trapezoid because it only has one set of parallel sides. | ## The Airplane Wing The airplane's wing only has one pair of parallel sides, so it is a trapezoid. |

## How to solve a Trapezoid

## Solve for X You first have to solve for X so you can plug it in and find the measurements for the sides. | ## Write out your equation. For this problem you are using the Trapezoid Mid-segment Theorem to solve it. So first, you write out your equation which is QR=1/2(LM+PN). | ## Plug in your numbers from the picture. To begin to solve for X, you need to plug in the numbers and variable given to you into the equation. |

## Solve for X

## Write out your equation.

## Simplify the parenthesis. You have to simplify the parenthesis before you do anything else, so you combine like terms to do that. | ## Get rid of the fraction. To make the problem easier so that you will have only nice numbers, get rid of the fraction. To get rid of the fraction you multiply both sides of the equation by 2. | ## Multiplied by Two. When you get rid of the fraction and multiply both sides by 2, you are left with this to solve for X. (Note: You do not multiply the numbers and variables inside the parenthesis by the 2.) |

## Simplify the parenthesis.

## Get rid of the fraction.

## Combine like terms. Subtract 2x from both sides to combine the variables. | ## Combine like terms again. Add 2 to both sides so that 2x is by itself. | ## Isolate X. To isolate X, divide 2 by both sides, getting rid of it next to the variable and dividing 6 by 2. |

## Real life examples of a geometric kite...

## A kite A kite that is used as a kids toy to fly in the air is a good example because it is exactly what a geometric kite is, except it flies, like in the picture. | ## The Stone in the ring The stone in the ring shown is a kite because the sides can be grouped into pairs of equal lengths. |

## How to solve a Kite...

## Solve for the missing angles. You have to use concepts learned in past chapter to find the answers for the missing angles. | ## Identify what you know. The measure of angle 1 is 90 degrees because diagonals of a kite are perpendicular. | ## Identify what you know. The measure of angle 3 is 52 degrees because corresponding parts of congruent triangles are congruent. |

## Solve for the missing angles.

## Identify what you know.

**diagonals of a kite are perpendicular.**

## Solve for the measure of angle 2 You are going to solve for angle 2 by using triangle sum theorem. 1. Set up everything to equal 108 2. Add 52 and 90 (combine like terms) 3. Subtract 142 from both sides of the equation 4. The measure of angle 2 equal 38 degrees | ## Your answer is... Angle 1 = 90 degrees Angle 2 = 38 degrees Angle 3 = 52 degrees |

## Solve for the measure of angle 2

1. Set up everything to equal 108

2. Add 52 and 90 (combine like terms)

3. Subtract 142 from both sides of the equation

4. The measure of angle 2 equal 38 degrees

## Video to help you better understand parallelograms....

## Citations

*Gift Box Clip Art at Clker.com*. Rollera LLC, 2003. Web. 25 Jan. 2016.

*- WeSharePics*. Carbone Smolan Agency, 23 Apr. 2014. Web. 25 Jan. 2016.

*Prezi.com*. Prezi, 2012. Web. 25 Jan. 2016.

*Wrigley.com*. Wrigley Jr. Company, 2012. Web. 25 Jan. 2016.

*Gardenworld*. Garden World Inc., 2012. Web. 25 Jan. 2016.

*Middle School Math: Real Life Applications and Historical Connections | NCEA*. NCEA, 2014. Web. 25 Jan. 2016.

*SchoolTube*. Shool Tube, 2011. Web. 25 Jan. 2016.