Circles

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Properties of Circles

What are attributes exactly? Attributes are characteristics that shapes have to help us put them into categories. A square for example has four sides which can be called a square’s attribute. This text will examine the geometric properties of circles.

Basic Properties of Circles

There are some geometric properties of a circle that we find out about: A curved line that is round is one of the properties of a circle.

A shape with no sides is one of the properties of a circle.

A shape with no vertices is another property of circles.

A shape that is the same distance from the centre is one of the properties of a circle.

Properties of Circles – Varying Features

As well as learning about the geometric properties of circles, we also learn about factors that circles may have, but that can vary. Circles also have varying features, such as: size, colour and direction

Properties of Circles – Additional Practice

Can you name the properties of a circle?

These are the main properties and the varying properties of circles:

Category of property “A circle …”
defining is round, has no sides or vertices.
non-defining can be of varying size, color and may face in any direction.

Following the video, there are interactive exercises and worksheets dealing with the question “what are the properties of circles”.

TranscriptCircles

“Nico, look at all those fun prizes in that machine! Do you think you can pick one up with the claw?” “Looks tricky, but let’s give it a try!” Nico pulled two prizes out of the claw machine. A play clock and a frisbee. “These two prizes are different, but the outside shape of them look the same!” “Yes, they are both round!” “Let’s make the claw machine even trickier by trying to get more prizes that have a round shape!” Circles. Shapes are two-dimensional figures that we can name based on their defining properties. Defining properties are characteristics that a shape must have. Let’s look at a circle. The defining properties of a circle are that it must be a closed shape that has a curved line that is round, no sides and no vertices. A circle also must be the same distance from the centre all the way around. If defining properties are characteristics a shape must have, what are non-defining properties? A non-defining property is something that a shape has, but doesn’t always have to be the same. Size is a non-defining property. A circle can be big, big, big! Or a circle can be small, small, small. Colour is another non-defining property. Circles can be any colour! Circles can also face many different directions. No matter how you turn it, a circle always looks the same! Let’s identify circles. Is this a circle? Start by looking at the shape. Is it a closed round shape made with a curved line? Yes, it is a closed round shape made with a curved line. Does it have sides? No, it doesn’t have any sides. Does it have any vertices? No, it doesn’t have any vertices. Is there an equal distance from the centre to the edge of the circle? Yes there is an equal distance from the centre to all parts of the outside of the circle. This is a circle. Let’s try this one. Is this a circle? Is it a closed round shape made with a curved line? Yes, it is a closed round shape made with a curved line. Does it have sides? No, it doesn’t have any sides. Does it have any vertices? No, it doesn’t have any vertices. Is there an equal distance around from the center? No, this shape is not an equal distance around from the centre. This shape is not a circle. Now that we know all the properties of a circle, let’s see if we can help Nico and Nia find more prizes that have a circular shape. Look at the claw machine. Can you point to the other prizes that have the outside shape of a circle? Here’s one! This stuffed cookie! This ring also makes the shape of a circle. And here's one more, this sparkling golden yoyo! Remember, shapes have defining and non-defining properties. A circle is a closed round shape that is made with a curved line. It doesn't have any sides or vertices but it must be equal distance all the way around the centre. A circle can be any size or colour and face in any direction. Nico and Nia see they have one token left. They can only go after one more prize! “I really hope we get the golden yoyo, Nico!" YAY! "YAY!"

Circles exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Circles.
• Recognising a circle.

Hints

Remember that a circle has to be the same distance from the centre all the way around. Here is an example.

Remember, circles must be closed shapes with one continuous curved line.

Is the shape the same distance from the centre to the edge, all the way around? This example is not a circle.

Solution

The pizza and the orange slice are circles.

The other images are not because a circle must be a closed shape, it must be the same distance from the centre all the way around, and be made from one continuous curved line.

• What is a circle?

Hints

To draw a circle, do we use a curved or straight line?

Sides are made from straight lines, not curved.

Solution
• All around a circle must be made from one continuous curved line.
• The number of sides of a circle has is always 0.
• A circle must be the same distance from the centre, all the way round.
• A circle is a flat 2D shape that is closed.
• True or False?

Hints

Which of these is a circle?

Are these all circles?

Solution

Four of the statements are true and three of the statements are false.

Some of the correct statements are about defining properties (e.g. it must be a closed shape); some of the statements are about non-defining properties (e.g. a circle can be any size or colour).

• How many circles?

Hints

Remember that circles have to be the same distance from the centre all the way around.

Remember that circles can be any colour and have any pattern on them.

Solution

There are 3 circles in this image.

These are the only shapes in the image that:

• Have one continuous curved line all the way around.
• Are closed shapes.
• Have the same distance from the centre to the edge all the way round.

• Looking for circular toys.

Hints

Does the shape have one continuous curved line all the way around?

Is the toy the same distance from the centre to the outside, all the way around?

There are three circular toys to find in total.

Solution

There are three circular toys: the cookie, the doughnut and the fidget toy.

These are circles because they:

• Are made from one continuous curved line.
• Are closed shapes.
• Are the same distance from the centre to the edge, all the way round.
• Seeing circles in real life.

Hints

The face of the shape is a circle if it is made up of a continuous curved line and is the same distance from the centre to the edge all the way round.

Imagine looking at the object from above. Do any of the faces look like a circle?

Solution
• The ice-cream is a cone shape. It has one circular face.
• The baked beans tin is a cylinder shape. It has two circular faces.
• The book is a cuboid shape. It has no circular faces.
• The pyramid is a square based pyramid shape. It has no circular faces.
• The drum is a cylinder shape. It has two circular faces.
• The gift box is a cube shape. It has no circular faces.