## Quadrilaterals Exploration

Today, you will complete an exploration about quadrilaterals. You will investigate the following essential questions:

Congruent = Figures that are the same size and the same shape; Angles that have the same measure.

Polygon = A closed figure with straight sides that intersect at points called vertices.

Parallel = Lines, rays, or segments that remain an equal distance from each other and never meet.

Perpendicular = Intersecting at a right (90 degree) angle.

Vertex = The point of intersection of two lines, rays, or line segments.

- What are the properties of quadrilaterals?
- How are quadrilaterals classified?

**Vocabulary terms**Congruent = Figures that are the same size and the same shape; Angles that have the same measure.

Polygon = A closed figure with straight sides that intersect at points called vertices.

Parallel = Lines, rays, or segments that remain an equal distance from each other and never meet.

Perpendicular = Intersecting at a right (90 degree) angle.

Vertex = The point of intersection of two lines, rays, or line segments.

**What are the properties of quadrilaterals?**

**Task 1:**Watch this video from Mr. Bowen about the properties of polygons. Do quadrilaterals share these properties?

**Task 2:**Use this applet to explore different kinds of quadrilaterals. Do you notice any common properties?

**Task 3:**Use this interactive from Geogebra to see if you can figure out the sum of the interior angles in a quadrilateral. Not sure? Try this one. Sill confused? Here is one more.

**How are quadrilaterals classified?**

**Task 4:**As you have seen, there are several types of quadrilaterals. How are they classified? Read below and examine the diagrams of quadrilaterals carefully.

Let's look more closely at each quadrilateral.

Parallelograms have opposite sides parallel and congruent. In this diagram, the red sides will never intersect and have the same length. The same is true of the blue sides. Notice that opposite angles are also congruent.

Rectangles are special kinds of parallelograms. They have all the properties of parallelograms (opposite sides are both parallel and congruent) plus one more: ALL their

*angles*are right angles (90 degrees).The rhombus, too, is a special type of parallelogram. In addition to having opposite sides parallel and congruent, the rhombus has one more property: ALL sides are congruent. Notice that just like parallelograms, opposite angles are congruent.

Squares are really special. Not only are they special kinds of parallelograms, they are special kinds of rectangles AND special kinds of rhombuses.That means, they have all the properties of parallelograms (opposite sides are both parallel and congruent), AND all the additional properties of rectangles (ALL angles are right angles) AND all the additional properties of rhombuses (ALL sides are congruent).

Take a look at this diagram that shows the relationships between these four types of quadrilaterals. Notice that a square can have lots of names -- a square is a polygon, quadrilateral, parallelogram, rhombus, rectangle... and a square!

Take a look at this diagram that shows the relationships between these four types of quadrilaterals. Notice that a square can have lots of names -- a square is a polygon, quadrilateral, parallelogram, rhombus, rectangle... and a square!

Let's now look at two types of quadrilaterals that are NOT parallelograms.

*Note: The arrow symbol means sides are parallel.*

The trapezoid (or trapezium if you live in the United Kingdom) must have four sides (as do all quadrilaterals) and has EXACTLY one pair of parallel sides. You are probably pretty familiar with the isosceles trapezoid. It is called isosceles because it has two sides that are congruent. However, trapezoids don't have to look like the red pattern block. The figure on the left is a scalene trapezoid because no sides are congruent, and the figure on the right is called a right trapezoid because it includes a right angle.

The kite has two pair of congruent sides (the red sides and the blue sides in the diagram above). Notice that it has NO parallel sides. What other properties do you notice about kites?

We can now add trapezoids and kites to our quadrilateral diagram. In the diagram below, the red markings indicate which sides are congruent.

Now that you are familiar with the different types of quadrilaterals and their special properties, let's see if you can apply your knowledge.

**Task 5:**How many different quadrilaterals can you make? Experiment with this interactive from nRich Math.

**Task 6:**Are you ready to test your ability to classify quadrilaterals? Take the Types of Quadrilaterals Challenge. Remember, some quadrilaterals can have multiple names!

**Task 7:**Reflect on what you have learned about quadrilaterals by completing this response form in Google Forms. Be sure to answer every question. Click submit when you are finished.

**Task 8:**Try these review games. You may have to click "enable flash" to begin.