4) Which shape can be classified as a rhombus?

Types of Quadrilaterals - Math Steps, Examples & Questions

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2D shapes Polygons Symmetry Line of symmetry Parallel lines Angles Types of angles

Math resources Geometry Quadrilateral

Types of quadrilaterals

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

Students will first learn about types of quadrilaterals as part of geometry in $4$ th grade.

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
Quadrilateral	Image	Sides	Angles	Symmetry
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 adjacent equal 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

Other properties of quadrilaterals:

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).

What are types of quadrilaterals?

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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:

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

Types of quadrilaterals examples

Example 1: square or rectangle

Correctly classify the following quadrilateral.

Types of Quadrilaterals - Square image 3 US

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.

Types of Quadrilaterals - Rhombus image 4 US

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

Quadrilateral $ABCD$ has $4$ equal, or congruent sides, as shown by the tick marks. It has $2$ pairs of equal angles, none of which are $90^{\circ}$ or right angles.

Quadrilateral $ABCD$ also has $2$ pairs of parallel sides.

Name the specific type of quadrilateral.

Since it has $4$ congruent sides but no right angles, quadrilateral $ABCD$ is a rhombus, not a square.

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.

Types of Quadrilaterals - Isosceles Trapezoid image 5 US

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

Since line $MN$ is a line of symmetry, you know that angle $A$ and angle $B$ are of equal measure.

Angles $D$ and $C$ are also equal. This also means that side $AD$ and side $BC$ are congruent. This shape has one pair of parallel sides; side $AB$ and side $DC$ .

Name the specific type of quadrilateral.

A quadrilateral with one pair of parallel sides is a trapezoid. Since this specific trapezoid also has $2$ pairs of equal angles, it is an isosceles trapezoid.

Example 4: classify quadrilaterals

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

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

Shape $A$ : $4$ equal angles (right angles), each pair of opposite sides are equal in length, $2$ pairs of parallel sides.

Shape $B$ : One pair of equal angles (right angles), one pair of parallel sides.

Shape $C$ : $4$ equal angles (right angles), $4$ equal sides, $2$ pairs of parallel sides.

Shape $D$ : $4$ equal angles (right angles), each pair of opposite sides are equal in length, $2$ pairs of parallel sides.

Shape $E$ : $2$ pairs of equal angles, each pair of opposite sides are equal in length, $2$ pairs of parallel sides.

Name the specific type of quadrilateral.

Shape $A$ : rectangle, parallelogram

Shape $B$ : trapezoid (specifically a right trapezoid)

Shape $C$ : square, rectangle, parallelogram, rhombus

Shape $D$ : rectangle, parallelogram

Shape $E$ : parallelogram

To answer the question, Shape $A$ and Shape $D$ can be classified as a rectangle.

Since a square has all of the properties of a rectangle, Shape $C$ can also be classified as a rectangle.

Example 5: name the shape

Types of Quadrilaterals - Irregular Quadrilateral image 7 US

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

The shape has $4$ sides, so it is a quadrilateral, but none of the sides are the same length. There are no angles of equal measure. The shape has no parallel sides or lines of symmetry.

Name the specific type of quadrilateral.

This shape is an irregular 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.

The left quadrilateral has $2$ pairs of congruent sides and $2$ pairs of congruent angles.

The right quadrilateral has $4$ pairs of congruent sides and $2$ pairs of congruent angles.

Both quadrilaterals have $2$ pairs of parallel sides. Therefore, they are both parallelograms. The sides of a rhombus are all equal in length, but it still classifies as a parallelogram as well.

Name the specific type of quadrilateral.

Although Ryan said one shape is a parallelogram and one is a rhombus, which is correct, he stated that only one shape is a parallelogram. So Maggie is correct since both shapes are parallelograms.

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

Incorrectly classifying quadrilaterals
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

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.

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.

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.

Types of Quadrilaterals image 12 US

Types of Quadrilaterals image 13 US

Types of Quadrilaterals image 14 US

Types of Quadrilaterals image 15 US

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

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.

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.

Types of quadrilaterals FAQs

What is a quadrilateral?

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.

The next lessons are

Perimeter
Symmetry
Angles in polygons
Surface area

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