Square shape

Here you will learn about a square shape, including what it is and how to identify it.

Students will first learn about a square shape as part of geometry in 4 th grade.

What is a square shape?

A square shape is a geometric shape with the following properties:

• Four congruent sides
• Four vertices
• Four right interior angles
• Two pairs of opposite sides that are parallel

For example,

Let’s look at each of the properties of a square.

• Four congruent sides:

The four sides of the square are all of equal length (congruent). Sometimes this is shown with a tick mark on each side, or the measurements of each side are given.

• Four vertices:

The sides of a square join at points called vertices. Since there are four sides, there are four vertices.

• Four right interior angles:

The sides of a square come together at a 90 -degree angle. This is why the sides that touch are considered perpendicular to each other.

• Two pairs of opposite sides that are parallel:

The opposite sides are always the same distance apart and will never intersect, which makes them parallel.

Since a four sided polygon will have four vertices, we can consider these properties together under the property of four equal sides when classifying.

Since the four right interior angles create two pairs of opposite sides that are parallel, we can also consider these together under the property of four right angles when classifying.

Because a square has all equal sides and angles, it is a regular polygon or more specifically a regular quadrilateral.

It also meets the definition of a rhombus, rectangle, and parallelogram.

What is a square shape?

Common Core State Standards

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

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

How to identify a square shape

In order to identify a square shape:

1. Look for a shape with four equal sides.
2. Decide if the shape has four right angles.

Square shape examples

Example 1: identifying a shape

Is the shape a square?

1. Look for a shape with four equal sides.

The shape has four equal sides.

2Decide if the shape has four right angles.

The sides do not form 90 -degree angles.

Two angles are obtuse…

And two angles are acute.

The shape does NOT have four right angles. It is NOT a square.

Example 2: identifying a shape

Is the shape a square?

Look for a shape with four equal sides.

The shape has four equal sides.

Decide if the shape has four right angles.

The sides form 90 -degree angles.

The shape is a square.

Example 3: identifying a shape

Is the shape a square?

Example 4: identifying a shape

The sides of a shape are: 4{~cm}, 4{~cm}, 4{~cm} and 4{~cm} . Is the shape a square?

Example 5: finding squares in geometric shapes

How many squares are formed by the geometric shape?

Look for a shape with four equal sides.

The shapes highlighted have four equal sides.

Decide if the shape has four right angles.

The sides form 90 -degree angles.

There are two squares in the geometric shape.

Example 6: finding squares in the real world

How many squares are in the image below?

Look for a shape with four equal sides.

The shapes in the windows have four equal sides.

Four parts of the window also come together to form a shape with four equal sides.

AND

Decide if the shape has four right angles.

The sides of the shapes meet at 90 -degree angles.

There are 21 squares in the image.

Teaching tips for square shape

• Printable worksheets are a great way for students to practice identifying or drawing squares.

• Point out squares in real life and encourage students to look for them as well. This should be an easy task, since there are many real world objects in the shape of a square. Seeing and talking about the properties of squares will help students remember and understand them.

Easy mistakes to make

• Confusing a square with a rectangle
  While a rectangle has many similar features as a square, it is not the same. A rectangle does not have to have four equal sides, but a square does. However, a square fits the definition of a rectangle, so is considered to be both.
  For example,
  
  

  

• Mistaking a rhombus for a square
  While a rhombus has many similar features as a square, it is not the same. A rhombus does not have to have four right angles, but a square does. However, a square fits the definition of a rhombus, so is considered to be both.
  For example,
  
  

  

Related quadrilateral lessons

• Quadrilateral
• Types of quadrilaterals
• Parallelogram
• Rectangle
• Rhombus
• Trapezoid

The next lessons are

• Perimeter
• Symmetry
• Angles in polygons

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