2D shapes

Here you will learn about 2D shapes, including the attributes of various 2D shapes and symmetry.

Students first learn about 2D shapes in kindergarten and first grade with their work in geometry, identifying and classifying shapes by their properties.

They expand their knowledge of 2D shapes as they progress through elementary and middle school.

What are 2D shapes?

2D shapes are flat shapes that can be drawn on a flat surface (or plane).

They have two dimensions, length and width, and have no thickness.

2D shapes can be grouped by the dimensions they have.

Here are some familiar 2D shapes.

Polygons

Polygons are 2D shapes made from straight lines that meet at points called vertices.

There are two different types of polygons.

Regular polygons	Irregular polygons
Regular polygons have equal side lengths and equal interior angles. Interior angles are the angles inside the polygon. Equilateral Triangle Square Regular Hexagon	Irregular polygons do not have all equal sides and do not have all equal angles. Interior angles are the angles inside the polygon. Right Triangle Rectangle Irregular Hexagon

Step-by-step guide: Polygons

Step-by-step guide: Regular polygons

Step-by-step guide: Irregular polygons

Symmetry

Symmetry is when an object can be divided into equal halves, where the two halves are mirror images of each other.

Line symmetry
Line symmetry is when an object can be divided in half with the two halves being reflections of each other. Both regular polygons and irregular polygons can have lines symmetry.
Square A square has 4 lines of symmetry.
Equilateral Triangle An equilateral triangle has 3 lines of symmetry. The lines of symmetry of a regular polygon are equal to the number of sides.
Trapezoid This trapezoid is not a regular polygon and has only 1 line of symmetry.

Step-by-step guide: Line symmetry

Step-by-step guide: Symmetry

Properties of 2D Shapes

Let’s look at the properties of some of the most common 2D Shapes.

Name of polygon	Properties of polygon
Equilateral triangle	● 3 vertices ● 3 equal sides ● 3 equal angles ● Each interior angle is 60^{\circ} ● 3 lines of symmetry ● 3 times of rotational symmetry within one full turn
Square	● 4 vertices ● 4 equal sides ● 4 equal angles ● Each interior angle is 90^{\circ} ● 4 lines of symmetry ● 4 times of rotational symmetry within one full turn
Regular pentagon	● 5 vertices ● 5 equal sides ● 5 equal angles ● Each interior angle is 108^{\circ} ● 5 lines of symmetry ● 5 times of rotational symmetry within one full turn
Regular hexagon	● 6 vertices ● 6 equal sides ● 6 equal angles ● Each interior angle is 120^{\circ} ● 6 lines of symmetry ● 6 times of rotational symmetry within one turn
Regular octagon	● 8 vertices ● 8 equal sides ● 8 equal angles ● Each interior angle is 135^{\circ} ● 8 lines of symmetry ● 8 times of rotational symmetry within one turn

Step-by-step guide: Pentagon (coming soon)

Step-by-step guide: Hexagon shape

Step-by-step guide: How to draw a hexagon

Step-by-step guide: Octagon (coming soon)

What are 2D shapes?

Common Core State Standards

How does this relate to kindergarten – 5 th grade math?

• Kindergarten: Geometry ( K.G.A.3)
  Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

• Grade 1: Geometry (1.G.A.2)
  Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape and compose new shapes from the composite shape.

• Grade 2: Geometry (2.G.A.1)
  Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

• Grade 4: Geometry (4.G.A.3)
  Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

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

How to use 2D Shapes

There are a lot of ways to use 2D shapes. For more specific step-by-step guides, check out the individual pages linked in the “What are 2D shapes?” section above or read through the examples below.

In order to identify a 2D shape, a polygon, or a regular polygon.

1. Recall the definition.
2. Explain how the 2D shape fits the definition.

2D shapes examples

Example 1: identifying polygons

What type of 2D shape is a stop sign?

1. Recall the definition.

A stop sign is a polygon with 8 sides.

2Explain how the 2D shape fits the definition.

Polygons that have 8 sides are called octagons. So, a stop sign is an octagon.

Example 2: identifying a polygon

Is a circle a polygon?

Example 3: identifying polygons

Is a pentagon a polygon?

Example 4: regular / irregular polygons

Is the parallelogram a regular polygon?

Example 5: symmetry

How many lines of symmetry does this rectangle have?

Explain how the 2D shape fits the definition.

In this case, the rectangle can be divided down the middle vertically and across the middle horizontally.

So there are 2 lines of symmetry.

Example 6: symmetry

Name the shape.

Explain how the 2D shape fits the definition.

The shape is an octagon because it has eight sides and eight angles. The sides and the angles are not equal, so it is also an irregular polygon. The shape is an irregular octagon.

Teaching tips for 2D shapes

• Instead of relying on worksheets, use manipulatives and real world objects in class so that students can see and understand the different shapes.

• Link art projects to 2D shapes and symmetry so that students can apply the math to creative projects.

• Provide students with cut-outs of the actual shapes so that they can measure the side lengths and angle measurements to develop their understanding of regular shapes versus irregular shapes.

• Include in lesson plans math centers where your learners can rotate through various 2D shape activities that are comprised of hands-on activities with pattern blocks, shape flashcards, and digital activities with math games so that students can learn shapes and their attributes.

• Reinforce essential vocabulary as it pertains to the geometrical shapes so students can recall the shapes names and see how they are used in real life.

Easy mistakes to make

• Confusing the different shapes
  For example, thinking that a pentagon is a hexagon or vice versa.

• Thinking that a rectangle is a regular polygon
  Squares are the only regular quadrilaterals. Rectangles have the same interior angles, but they do not have the same side lengths.

• Thinking that figures can’t have more than one line of symmetry
  2D shapes can have more than one line of symmetry or no lines of symmetry.

• Rotational symmetry/lines of symmetry
  Lines of symmetry are often confused with rotational symmetry. A line of symmetry on a two-dimensional shape divides the shape equally into two symmetrical pieces. Rotational symmetry is the number of times a shape fits into itself when rotated around its center.

• Thinking that an irregular hexagon is not a hexagon
  If students have too much exposure to regular hexagons and not enough of irregular hexagons, they may believe that a regular hexagon is the only type of hexagon. Be sure to vary their exposure to hexagonal shapes and give them opportunities to work with and draw hexagons that are not regular. This applies to all other types of polygons as well.

The next lessons are

• Triangles
• Quadrilateral
• Perimeter

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

Find out how we can help your students achieve success with our math tutoring programs.