### Unit 5: Polygons and Quadrilaterals

A polygon is a shape that has no curves. In this unit, we will focus on quadrilaterals, which are polygons with four sides. While each has their own set of characteristics, they share some properties with other quadrilaterals.

**Completing this unit should take you approximately 4 hours.**

Upon successful completion of this unit, you will be able to:

- calculate the measure of interior angles of polygons;
- calculate the measure of exterior angles of polygons;
- use various theorems to algebraically calculate missing sides and/or angles in polygons; and
- classify quadrilaterals.

### 5.1: Sum of Interior Angles of a Polygon

Before we can begin studying polygons, we need to develop an understanding of the language of polygons and quadrilaterals.

Read this article, which reviews types of quadrilaterals and how to calculate the sum of polygon angles.

Now we are ready to explore the interior angles of a polygon in more detail. Watch this video for examples of how to determine the sum of the interior angles in a polygon.

### 5.2: Sum of Exterior Angles of a Convex Polygon

In addition to determining the sum of the interior angles of a polygon, we can determine the sum of the exterior angles in a convex polygon.

Watch this video to learn how to perform this calculation and to see examples.

Then, complete this assessment, which includes the sum of exterior angles of a polygon and the sum of interior angles of a polygon.

### 5.3: Parallelograms

A parallelogram is a type of quadrilateral we encounter often. A parallelogram is a quadrilateral where two pairs of sides are parallel. In this section, we discuss the properties of parallelograms and how to classify them.

Read this article and watch the videos, which review the structure and properties of parallelograms. Pay attention to the list of theorems that pertain to parallelograms. These theorems are useful when solving for unknown side lengths or angles. Closely read the sections on measuring angles and solving for unknown values. Be sure to read examples 1–3.

Then, complete review questions 1, 4, 5, 16, 17, 18, and 19 and check your answers.

We can classify different types of parallelograms based on their properties. Read this article and watch the video. Pay attention to the definitions for rectangle, rhombus, and square.

Then, complete review questions 4–15 and check your answers.

### 5.4: Trapezoids

A trapezoid is a different type of quadrilateral where only one pair of sides is parallel.

Read this article and watch the video. Pay attention to the special form of the midsegment theorem as it applies to trapezoids. Closely read examples 1–5.

Then, complete review questions 2, 3, and 8 and check your answers.

### 5.5: Kites

The last special type of quadrilateral we explore is the kite. One example of a kite quadrilateral is the traditional kite shape you may have flown as a child. But there are many other examples of the quadrilateral kite shape.

- Read this article and watch the two embedded videos which describe the properties of kites and shows various examples. Pay attention to the examples on measuring angles, using the Pythagorean theorem, and finding the missing angle. Closely read examples 1–3.

After you have reviewed the material, complete review questions 1, 2, 7, and 8 and check your answers.

### 5.6: Coordinate Geometry

Finally, we review an overview of the properties of quadrilaterals.

Watch these two videos on quadrilaterals and their properties.

Then, complete this assessment to review your knowledge of quadrilaterals and check your answers.