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Basics on the topic Quadrilaterals
Quadrilaterals – Definition
We might have learnt about some different types of shapes before, but now let's focus on one type in particular, quadrilaterals. What is a quadrilateral you ask? A quadrilateral is a shape with four sides. It has defining and non defining properties.
Quadrilaterals – Properties
A quadrilateral is a special flat, four sided shape. A quadrilateral is also a polygon. The ‘quad’ part of the quadrilateral meaning refers to the number four. So, how many sides does a quadrilateral have? It has four. In order for a shape to meet the definition of quadrilateral, it must have the four properties of a quadrilateral:
- It must have four straight sides,
- Four angles,
- Be fully closed,
- And be two-dimensional, or flat.
These are called defining quadrilateral attributes and can never change. They are characteristics that have to stay the same.
However, some quadrilateral characteristics can change and the shape can still be called a quadrilateral.These characteristics are called non-defining attributes. So, quadrilateral polygons can be any colour, size, or face in any direction.
What do quadrilaterals look like? A quadrilateral can look like many things. Let’s use an example to see if we can spot what one looks like. Is this a picture of a quadrilateral?
First, we need to determine if this shape has all four properties of quadrilaterals. It has four straight sides. It has four angles. It is closed and it's two-dimensional. This shape is a quadrilateral because it meets all four defining attributes
Quadrilaterals – Summary
Remember, the definition of a quadrilateral is a shape that must meet these requirements:
|It must have four straight sides.
|It must have four angles.
|It must be fully closed.
|It must be two-dimensional or flat.
However, the size, colour, and direction of a quadrilateral can change.
Have you practised with pictures of quadrilateral shapes yet? On this website, you can also find examples of quadrilateral shapes, quadrilateral worksheets, and interactive exercises for KS2.
Nico and Nia have bought glow-in-the-dark shapes to stick to the attic ceiling! They can't wait to put them up, but first they must read the instructions. The directions say to put extra sticky-tack on the quadrilaterals but Nia and Nico don't know what a quadrilateral is! Let's help them by learning about quadrilaterals! Quadrilaterals are special flat, four sided shapes. The quad part of the word, quadrilateral, means four. In order for a shape to be called a quadrilateral, these things must always be true: It must have four straight sides, four angles, four vertices, be fully closed and be two-dimensional, or flat. These are called the shape's properties and can never change, if a shape is to be called a quadrilateral. They are characteristics that have to stay the same. However, some characteristics can change and the shape can still be called a quadrilateral. These are features that a quadrilateral may have. Quadrilaterals can be any colour size, or face any direction. Let's use this checklist to see which glow in the dark stickers are quadrilaterals that need extra sticky-tack. First, we need to determine if this shape has all the properties that are characteristic of a quadrilateral. It has four straight sides. It has four angles. It has four vertices. It is closed and it's two dimensional. This shape is a quadrilateral because it has all these properties. Let's put extra sticky-tack on it. Now look at this shape, does it have all the properties of a quadrilateral? It does not have four straight sides, it has ten. This shape does not have four sides so we can stop checking as it does not have all the requirements. This shape does not need extra sticky-tack. Let's look at this shape now. Does it have all the properties of a quadrilateral? It has four straight sides. It has four angles. It has four vertices. It is closed and it's two dimensional. This shape is a quadrilateral because it has all of these properties. Let's put extra sticky-tack on it. Now, try this shape on your own. Use the checklist to see if the shape has all the properties of a quadrilateral. Is this shape a quadrilateral? This shape is not a quadrilateral. While it is closed and its sides are straight, it has more than four sides and more than four vertices. It's also not flat, it's three dimensional! So this shape does not get extra sticky-tack. While Nico and Nia continue to sort through the other shapes, let's review. Today we learned about quadrilaterals. In order for a shape to be called a quadrilateral, it must have these important properties: four straight sides, four angles, four vertices, be fully closed and be two-dimensional. However, the size, colour and direction of a quadrilateral can change. "That's the last one. Nico, can you hit the lights?" "I think I want to make a wish!"
What are the properties of a quadrilateral?Hints
Remember, if a shape has more than 4 sides, it can't be a quadrilateral.
Remember if a shape is 3D and not flat, it can't be a quadrilateral.Solution
- First, check if the figure has 4 straight sides.
- Next, check for 4 vertices.
- Check for 4 angles.
- Then, see if the figure is closed with no open areas.
- Finally, see if the figure is flat and not 3D.
Which of the following is a quadrilateral?Hints
- How many sides does the figure have?
- Are the sides straight?
How many vertices does the figure have?
Is the figure 2D or 3D?Solution
Every quadrilateral must:
- Have 4 straight sides
- Have 4 vertices
- Be closed
- Be 2D (flat)
If one of these is not true, then it is not a quadrilateral.
Which of the following is not a property of a quadrilateral?Hints
You are looking for the answer that is not a characteristic of quadrilaterals.
This is a quadrilateral.
This is not a quadrilateral.
This is an example of a 3D, or solid, shape which is not a quadrilateral.Solution
The answer is 3D as quadrilaterals are not 3D.
- 4 straight sides
- 4 corners
- are closed
- are 2D or flat
Determine which shapes are quadrilaterals.Hints
First check how many sides a figure has to determine if it is a quadrilateral.
Next check if it is 2D or 3D to determine if it is a quadrilateral.Solution
- 4 straight sides
- 4 vertices
- 2D or flat
Determine if the shapes are quadrilaterals or not.Hints
How many sides does the shape have?
Are those sides straight or curved?
This is an example of a quadrilateral.Solution
Here are the quadrilaterals. They:
- have 4 straight sides
- have 4 vertices
- are closed
- are 2D or flat
Name the quadrilaterals.Hints
A square has 4 sides of equal length.
The opposite sides of a rectangle are equal.
A quadrilateral must be a closed 2D shape with 4 corners and 4 sides.Solution
A quadrilateral must be a closed 2D shape with 4 corners and 4 sides. The picture shows the shapes matched with the names.
The shape above that is not a quadrilateral is a pentagon - a 2D shape with 5 sides.