Squares and Rectangles
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Basics on the topic Squares and Rectangles
Rectangles and Squares
Learn about squares and rectangles and think about how squares and rectangles differ from one another as well as what squares and rectangles have in common.
Rectangles and Squares – Similarities and Differences
Squares and rectangles are 2D shapes. 2D (two-dimensional) shapes are flat figures with two dimensions. We know that squares and rectangles are both 2D shapes but what are some similarities and differences between squares and rectangles?
You may wonder what do squares and rectangles have in common? We know they are both 2D shapes but they also share some other properties. The properties of rectangles and squares that are the same are:
- they both have 4 sides
- they both have 4 vertices
- they both have 4 right angles
They are not exactly the same though as squares must have 4 sides that are all exactly the same length whereas rectangles have 2 pairs of sides that are the same length. A square can be called a special type of rectangle.
Rectangles and Squares – Examples
Properties of a square
Properties of a rectangle
Squares and rectangles also share properties that we can call ‘non-defining’. This means that these features can change but the shape will still be a square or rectangle as long as it has all of the properties it needs to be called that shape. For example, the colour, size or orientation could change but it would not change the defining properties of the shape.
Rectangles and Squares – Worksheets
The table below shows the main properties of squares and rectangles.
|All sides have the same length.
|Opposite sides have the same length.
|4 right angles
|4 right angles
To practise further, have a look at our rectangles and squares worksheets at the end of the video and learn more about the properties of squares and rectangles (worksheets). We also have a range of interactive exercises featuring squares and rectangles as well as further 2D shapes.
Frequently Asked Questions regarding Squares and Rectangles
Transcript Squares and Rectangles
Nico and Nia are working at the art gallery. New paintings just arrived and they are in charge of hanging them on the wall. We can help by finding frames that are in the shape of “ Squares and Rectangles”.
Squares and rectangles are shapes. Shapes are two-dimensional figures that we can name based on their “properties”. Properties are characteristics that a shape MUST HAVE. First, let’s look at a square. The properties of a square are that it must be a closed shape and have four sides that are ALL the SAME length, four corners or vertices, and four RIGHT angles. A right angle is the opening in a shape that makes another little square on the INSIDE corner. Let's count the right angles in a square: one, two, three, four. Now, let’s look at a rectangle. A rectangle looks a lot like a square. The properties of a rectangle are that it must have four sides that are equal on opposite sides. THIS side is equal to THIS one, and THIS side is equal to THIS one. A rectangle must also have four corners or vertices and four right angles. Because squares and rectangles share most properties, we can group them together. Squares and rectangles can also have other features. These features don't always have to be the same. They can change and the shape would still remain that shape. Size is an example.. Squares and rectangles can be big, big, BIG, or they can be small, small, small. Colour is another example. Squares and rectangles can be ANY colour! They can also face in any direction! Let’s identify squares and rectangles! Is this shape a square or a rectangle? Let's start with counting the sides, it has one, two, three, four sides. How many of the sides are the same length? All four sides are the same length! This side is equal to this one, and this side is equal to that one. Now count the vertices. It has one, two, three, four vertices. Finally, count the right angles on the inside. It has one, two, three, four right angles.
Is this shape a square or a rectangle? This shape is a SQUARE, BUT this shape can ALSO be called a rectangle! How about this shape? Is this shape a square or a rectangle? Start by counting the sides. One, two, three, four. How many sides are the same length? Two. THIS side is equal to THIS one, and THIS side is equal to THIS one. Now count the vertices. One, two, three, four. Finally, count the right angles. How many angles are right angles? Four! Is this shape a square or a rectangle? This shape is a rectangle! Here’s one more! Is this shape a square or a rectangle? NO! This shape is not a square or a rectangle! This shape only has three sides. Now that we know all of the properties of squares and rectangles, let’s help Nico and Nia in the art gallery. Look at the pictures at the gallery. Can you point to all of the paintings that have a frame that is either a square or a rectangle? Here, THIS frame has all of the properties of a square, and THIS frame has all of the properties of a rectangle! This frame is a rectangle, even though it is turned. Here's the last rectangle right here! Remember, shapes have properties which are features that they must have. Squares and rectangles are closed shapes that ALWAYS have four sides, four corners or vertices, and four right angles. Squares have four sides all the same length, and rectangles have two opposite sides that are the same length. But, they can be any size, or colour, and face in any direction. “Look Nia!” “Here’s one more picture to hang!” “Ooohhhh, that’s my favourite!!!”
Squares and Rectangles exercise
Count the squares and rectangles.Hints
Make sure to check for right angles. Squares and rectangles MUST have 4 right angles.
Are opposite sides equal? Rectangles and squares have opposite sides that are equal in length.
Check the shapes that are in different orientations. Are any of these squares or rectangles?Solution
There are 3 squares and 2 rectangles, so in total there are 5.
Facts about squares and rectangles.Hints
Squares and rectangles have 4 right angles.
Squares and rectangles have 4 vertices.Solution
All squares have 4 right angles. TRUE.
A square can have 5 vertices. FALSE. A square always has 4 vertices.
Rectangles can be any colour and size. TRUE.
All rectangles have 4 sides. TRUE.
Some rectangles have 3 sides in total. FALSE. Rectangles have 4 sides in total.
Identify the squares and rectangles.Hints
Remember that squares have 4 sides equal in length.
Remember that rectangles have 4 straight sides with opposite sides that are equal in length.Solution
There are 5 squares and 3 rectangles in the picture. Here the squares are outlined in red and the rectangles are outlined in yellow.
Which shapes are rectangles?Hints
A rectangle is a closed shape. That means the outside of the shape must start and end at the same point.
Remember, a rectangle must have 4 right angles and opposite sides that are equal in length.Solution
The playing card, the TV, and the sweet are all rectangles.
The mountain, the dartboard, the circle, the diamond, and the incomplete rectangle are not rectangles.
How many squares and rectangles?Hints
Look at the frame that has been tilted - it is still a rectangle!
Remember that one of the properties of squares and rectangles is that they must have 4 sides, with opposite sides equal in length.Solution
The fruit and the sunset are in square frames.
The camels and the sunflowers are in rectangle frames.
How many squares?Hints
Are there any squares within the squares? In this example, there are 8 small squares, but 3 larger squares within the rectangle.Solution
This image shows where 4 of the squares are hidden in the green shape.
In the red shape there are 10 squares.
In the blue shape there are 5 squares.
In the green shape there are 14 squares.
In the orange shape there are 3 squares.