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?

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.

Types of quadrilaterals examples

Example 1: square or rectangle

Correctly classify the following quadrilateral.

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.

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.

Example 4: classify quadrilaterals

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

Example 5: name the shape

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?

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.

Related quadrilateral lessons

• Quadrilateral
• Parallelogram
• Rectangle
• Rhombus
• Square shape
• Trapezoid

The next lessons are

• Perimeter
• Symmetry
• Angles in polygons
• Surface area

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