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Categories of quadrilaterals based on sides and angles.
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Have you ever heard of a yurt? Take a look at this dilemma.

“This is very cool!” Marcus exclaimed when looking through a book on different types of houses.

“What do you see?” Lynne asked leaning over her desk to look at the book that Marcus was holding.

Lynne and Marcus are both students in Mrs. Patterson’s World Cultures class. Like Jaime, they are also working on projects. Marcus has discovered a yurt. A yurt is a type of home common in Mongolia. There is a lattice structure that is built and then a canvas is used to cover the frame.

“That is cool, what is it?” Lynne asked.

“It’s called a yurt. I think that this is what I am going to do my project on,” Marcus said, studying the picture.

Marcus took out a piece of paper and a pencil and he began to draw the lattice of the yurt.

As Marcus draws his design, take a look at the lattice and hunt for the quadrilaterals that are used in the design. In this Concept, you will learn all about different types of quadrilaterals so that you will be able to identify the ones that Marcus will need to use.

### Guidance

A quadrilateral is any four-sided figure. In the word “quadrilateral”, we find the word “quad” which means four. This means that any four-sided figure is considered a quadrilateral. Now, there are different types of quadrilaterals that we are going to learn about in this lesson.

We can say that a quadrilateral is any four-sided figure. We could consider this an umbrella category meaning that there are different types of quadrilaterals that we can identify in a specific way even though they are still quadrilaterals too.

Let’s look at identifying the types of quadrilaterals.

The first type of quadrilateral to learn about is called a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel and congruent. Here is a picture of a parallelogram.

When you look at this picture, you can see that the opposite sides of the figure are parallel. They are also the same length-meaning congruent .

There are three main kinds of parallelograms.

Parallelograms can be plain old parallelograms like the one in the picture. They can also be rectangles, squares and rhombi.

A rectangle is a parallelogram with four right angles, where opposite sides are congruent and parallel. You have been looking at rectangles for a long time, but now you need to notice that there are specific properties that make a rectangle a rectangle.

A rhombus is a parallelogram with four congruent sides, but not necessarily four right angles. A rhombus can look like a square, but while a square is always a rhombus, a rhombus is not necessarily a square. A rhombus can only be a square if it has four right angles.

A square is a parallelogram too. The big difference between a square and a rectangle is that a square has four congruent sides. It also has four right angles though just like a rectangle.

There is one other type of quadrilateral. This quadrilateral is NOT a parallelogram. It is a special kind of quadrilateral. It is called a trapezoid . A trapezoid is a quadrilateral with one pair of opposite sides parallel.

#### Example A

A parallelogram with all sides congruent and has four right angles.

Solution: Square

#### Example B

A parallelogram with two pairs of congruent sides and four right angles.

Solution: Rectangle

#### Example C

A quadrilateral with opposite sides congruent and one pair of parallel sides.

Solution: Trapezoid

Now let's go back to the dilemma from the beginning of the Concept.

Now look at the picture of the yurt once again.

In looking at this diagram, it looks like there is a square being used as the design of the lattice. Examine this more closely and you will see that the sides of each figure created by the lattice are all equal. This may make you think that this is definitely a square. However, if you look at the angles, the angles are not right angles. Therefore, it can’t be a square. In fact, it is actually a rhombus. Remember that a rhombus has four sides of equal length, but it does not have to have right angles.

### Vocabulary

A quadrilateral is a closed figure with four sides and four vertices.
Trapezoid
A trapezoid is a quadrilateral with exactly one pair of opposite sides parallel.
Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides.
Rhombus
A rhombus is a quadrilateral with four congruent sides.
Rectangle
A rectangle is a quadrilateral with four right angles.
Square
A square is a polygon with four congruent sides and four right angles.
Congruent
Congruent figures are identical in size, shape and measure.

### Guided Practice

Here is one for you to try on your own.

Solution

Looking at this pool, we can begin to think about the different characteristics of the pool. First, it has opposite sides that are congruent and parallel. It also has four right angles, this makes this figure a rectangle.

### Explore More

Directions: Identify each quadrilateral based on the description provided.

1. A figure with four equal sides and four right angles.
2. A figure with opposite sides congruent and parallel.
3. A figure with opposite sides congruent and parallel and four right angles.
4. A figure with four sides.
5. A figure with four equal sides which may or may not have four right angles.

Directions: Use what you have learned about quadrilaterals to answer each of the following questions true or false.

1. A quadrilateral can be any four sided figure.
2. A rectangle is also a parallelogram, but a parallelogram is not necessarily a rectangle.
3. A square is never a parallelogram.
4. A rhombus can be a square.
5. A square is always a rhombus.
6. A rhombus is a parallelogram.
7. A quadrilateral is a type of parallelogram.
8. A trapezoid has opposite sides parallel and congruent.
9. What does the sum of the angles of a quadrilateral add up to be?
10. What are all four angle measures of a rectangle?
11. What are all four angle measures of a square?

### Vocabulary Language: English

Congruent

Congruent

Congruent figures are identical in size, shape and measure.
Kite

Kite

Parallelogram

Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides.

A quadrilateral is a closed figure with four sides and four vertices.
Rectangle

Rectangle

A rectangle is a quadrilateral with four right angles.
Rhombus

Rhombus

A rhombus is a quadrilateral with four congruent sides.
Square

Square

A square is a polygon with four congruent sides and four right angles.
Trapezoid

Trapezoid

A trapezoid is a quadrilateral with exactly one pair of parallel opposite sides.