Here we will learn about types of quadrilaterals, including their names and properties and how to classify them.

## What are types of quadrilaterals?

Quadrilaterals are four-sided 2D shapes. The word quadrilateral comes from the latin word quadri meaning four and latus (lateral) meaning side. There are many different types of quadrilaterals.

For example,

Properties

Square

● Four equal sides

● Each pair of
opposite sides
are parallel

● Four equal
angles (90^{\circ})

● Four lines of
symmetry

Rectangle

● Two pairs of
equal sides

● Each pair of
opposite sides
are parallel

● Four equal
angles (90^{\circ})

● Two lines of
symmetry

Parallelogram

● Two pairs of
equal sides

● Each pair of
opposite sides
are parallel

● Two opposite
pairs of equal
angles

● No lines of
symmetry

Rhombus

● Four equal sides

● Each pair of
opposite sides
are parallel

● Two opposite
pairs of equal
angles

● Two lines of
symmetry

Kite

● Two pairs of
sides

● One pair of
equal angles

● One line of
symmetry

Trapezoid
(Trapezium)

● One pair of
parallel sides

Isosceles
Trapezoid:
● Two pairs of
equal angles

Non-isosceles:
● No equal angles

Right Trapezoid:
● One pair of
right angles (90^{\circ})

● One line of
symmetry
(isosceles
trapezoid)

● No lines of
symmetry
(if not
isosceles)

Irregular

● No equal sides

● No pairs of
parallel sides

● No equal
angles

● No lines of
symmetry

• The sum of the interior angles of a quadrilateral total 360^{\circ} .

• Quadrilaterals can be convex or concave.
A convex quadrilateral is a polygon with all interior angles less than 180^{\circ} . All quadrilateral shown in table above.

• A concave quadrilateral has at least one angle that is greater than 180^{\circ} (or a reflex angle).

## Common Core State Standards

How does this relate to 4 th grade math and 5 th grade math?

• Grade 4 – Geometry (4.G.2)
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

• Grade 5 – Geometry (5.G.3)
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

• Grade 5 – Geometry (5.G.4)
Classify two-dimensional figures in a hierarchy based on properties.

## How to classify a quadrilateral

In order to classify a quadrilateral:

1. Examine the properties of the quadrilateral, including side lengths and angle measurement.
2. Name the specific type of quadrilateral.

### Example 1: square or rectangle

1. Examine the properties of the quadrilateral, including side lengths and angle measurement.

This quadrilateral has 4 sides. The opposite sides are the same length, as shown by the tick marks. It also has 4 angles of equal measure, all of which are 90^{\circ} or right angles. This quadrilateral also has 2 pairs of parallel sides.

2Name the specific type of quadrilateral.

Since the sides are not all the same length, this quadrilateral is a rectangle, not a square. Since the shape has two pairs of parallel sides, it is also a parallelogram.

### Example 2: parallelogram or rhombus

Determine what type of quadrilateral shape ABCD is.

Examine the properties of the quadrilateral, including side lengths and angle measurement.

Name the specific type of quadrilateral.

### Example 3: quadrilateral with symmetry

The polygon below is a quadrilateral. The quadrilateral has one line of symmetry along MN . By examining its properties, determine the type of quadrilateral.

Examine the properties of the quadrilateral, including side lengths and angle measurement.

Name the specific type of quadrilateral.

Which of the following shapes can be classified as a rectangle?

Examine the properties of the quadrilateral, including side lengths and angle measurement.

Name the specific type of quadrilateral.

### Example 5: name the shape

Examine the properties of the quadrilateral, including side lengths and angle measurement.

Name the specific type of quadrilateral.

### Example 6: word problem

Maggie drew 2 shapes. She says they are both parallelograms. Her friend Ryan said only one is a parallelogram but the other is a rhombus since it has 4 equal sides. Who is correct?

Examine the properties of the quadrilateral, including side lengths and angle measurement.

Name the specific type of quadrilateral.

### Teaching tips for types of quadrilaterals

• Utilize visual aids such as posters, charts, or flashcards to display different types of quadrilaterals. This will help students visualize the properties of quadrilaterals and make comparisons.

• Create a worksheet with various quadrilaterals shown as shapes or objects.
• Ask students to identify and label each type of quadrilateral correctly.
• Provide additional challenge by including shapes that have characteristics of multiple types of quadrilaterals, requiring students to analyze the properties carefully.

• Provide students with practice problems that include pictures or real-life examples of objects or buildings that resemble different types of quadrilaterals. Ask them to identify and classify the objects, explaining why they think it belongs to a particular category.

### Easy mistakes to make

Sometimes, shapes can have similarities and overlap between different types of quadrilaterals, leading to confusion. It’s important to carefully examine the properties of quadrilaterals to classify them correctly.

• Confusing a square with a rectangle
While all squares are rectangles, not all rectangles are squares. A square has equal sides, whereas a rectangle has opposite sides of equal length.

• Mistaking a rhombus for a square
A rhombus has four equal sides, but its angles are not right angles like in a square.

### Practice types of quadrilaterals questions

1) Which of the following classifications does the quadrilateral NOT fit?

Rectangle

Square

Parallelogram

Trapezoid

This shape has 4 equal sides and 4 angles of equal measure. The 4 angles are right angles ( 90^{\circ} ). It also has 2 pairs of parallel sides. Therefore this is a square.

Based on its properties, it also classifies as a rectangle and a parallelogram. A trapezoid has only one pair of parallel sides, so this shape is not a trapezoid.

2) Determine what type of quadrilateral shape ABCD is.

Rhombus

Parallelogram

Trapezoid

Kite

This shape has 2 pairs of opposite sides that are equal and 2 pairs of angles of equal measure. It has no right angles. It has 2 pairs of parallel sides. Therefore this is a parallelogram.

3) The quadrilateral shown below has one line of symmetry on the dotted line. Name the quadrilateral.

Rectangle

Right trapezoid

Isosceles trapezoid

Parallelogram

This shape has one pair of parallel sides. Since it also has one line of symmetry and 2 pairs of equal angles, this is an isosceles trapezoid.

4) Which shape can be classified as a rhombus?

The second shape has 4 equal sides, 2 pairs of equal angles, and 2 pairs of parallel sides. Therefore it is a rhombus.

5) Use the diagram to classify the quadrilateral ABCD .

Hexagon

Kite

Rhombus

Parallelogram

Quadrilateral ABCD has two pairs of adjacent sides of equal length, and one pair of angles of equal measure. It also has one line of symmetry. It has no parallel sides. Quadrilateral ABCD is a kite.

6) The quadrilateral below can be classified as…

a parallelogram, rectangle, and square.

a parallelogram, rectangle, and rhombus.

a rectangle.

a parallelogram and rectangle.

This quadrilateral has 2 pairs of opposite sides that are equal, 4 right angles, and 2 pairs of parallel sides. That means it can be classified as a rectangle but also as a parallelogram.

A quadrilateral is a polygon with four sides.

How many types of quadrilaterals are there?

There are several types of quadrilaterals, but some common ones include squares, rectangles, parallelograms, trapezoids, and rhombuses.

What is a square?

A square is a quadrilateral with four equal sides and four right angles.

What is a rectangle?

A rectangle is a quadrilateral with four right angles, but its opposite sides are equal in length.

What is a parallelogram?

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.

What is a trapezoid?

A trapezoid is a quadrilateral with one pair of parallel sides. The other two sides are not parallel.

What is a rhombus?

A rhombus is a quadrilateral with four equal sides. It also has opposite angles that are equal.

Are all squares also rectangles?

Yes, all squares are rectangles because they have four right angles. However, not all rectangles are squares since rectangles can have sides of different lengths.

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