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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.
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 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 Equilateral Triangle Square Regular Hexagon | Irregular polygons do not have all equal Right Triangle Rectangle Irregular Hexagon |
Step-by-step guide: Polygons
Step-by-step guide: Regular polygons
Step-by-step guide: Irregular polygons
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 |
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
Let’s look at the properties of some of the most common 2D Shapes.
Name of polygon | Properties of polygon |
---|---|
Equilateral triangle |
● 3 vertices |
Square |
● 4 vertices |
Regular pentagon |
● 5 vertices |
Regular hexagon |
● 6 vertices |
Regular octagon |
● 8 vertices |
Step-by-step guide: Pentagon
Step-by-step guide: Hexagon
Step-by-step guide: How to draw a hexagon
Step-by-step guide: Octagon
How does this relate to kindergarten – 5 th grade math?
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.
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEWhat type of 2D shape is a stop sign?
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.
Is a circle a polygon?
Recall the definition.
A polygon is a 2D shape made up of straight lines that meet at points called vertices.
Explain how the 2D shape fits the definition.
A circle is a 2D shape, but it is not made up of straight lines, so it is not a polygon.
Is a pentagon a polygon?
Recall the definition.
A polygon is a 2D shape made up of straight lines.
Explain how the 2D shape fits the definition.
A pentagon is a 2D shape made up of straight lines, so it is a polygon.
Is the parallelogram a regular polygon?
Recall the definition.
Regular polygons have equal side lengths and equal interior angles.
Explain how the 2D shape fits the definition.
The parallelogram does not have equal side lengths and does not have equal interior angles, so it is not a regular polygon.
How many lines of symmetry does this rectangle have?
Recall the definition.
Line symmetry is when an object can be divided in half, with the two halves being mirror images or reflections of each other.
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.
Name the shape.
Recall the definition.
Octagons are polygons with 8 sides.
Irregular polygons are polygons that do not have equal sides and equal angles.
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.
1. Which figure below represents a regular polygon?
Regular polygons have equal side lengths and equal interior angles.
The only figure that has equal side lengths and equal interior angles is the regular hexagon.
2. Which polygon has 5 vertices?
The pentagon has five vertices.
The vertices are the corners of the shape.
3. Which 2D shape is an irregular hexagon?
An irregular hexagon is a 6 sided shape that does not have equal side lengths or equal interior angles.
This polygon was the only one with 6 sides.
4. Which shape has 4 lines of symmetry?
A square is a regular polygon with four equal sides and four equal interior angles.
So it will have four lines of symmetry.
A rectangle will only have two lines of symmetry, a kite and a parallelogram have no lines of symmetry.
5. How many lines of symmetry does this 2D figure have?
By definition, line symmetry is when an object can be divided in half, with the two halves being mirror images or reflections of each other.
In this case, the snowflake has six lines of symmetry.
6. Which of the following shapes has only two lines of symmetry?
No lines of symmetry.
Two lines of symmetry
No lines of symmetry
One line of symmetry
By definition, polygons are enclosed 2D shapes made up of straight lines that meet at points. If a shape has a curved line edge, it will not be a polygon.
Perimeter is the distance around the shapes, so you can just add up the side lengths. The area is the space within the shapes. There are various formulas you will learn to find the areas of shapes such as triangles, squares, rectangles, and parallelograms.
The sum of the interior angles of a polygon is always the number of sides minus 2 times 180 . You will learn this as you move into high school.
A cuboid is another name for a cube, which are 3D shapes where each face is a square.
A rhombus is a parallelogram, so opposite sides are equal and opposite sides are parallel, and in addition to that, all four sides are equal.
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