Infinite number A circle has an infinite number of lines of symmetry since any straight line passing through the centre of the circle will be a line of symmetry.

Contents

## What symmetry does a circle have?

Lines of Symmetry in a Circle – A circle has its diameter as the line of symmetry, and a circle can have an infinite number of diameters. Hence, a circle has infinite lines of symmetry. Thinking Out Of the Box!

- How many lines of symmetry does a human body can have?
- Is your mirror image symmetric to you?

Important Notes

- A circle has infinite axes of symmetry.
- A circle has rotational symmetry.
- If any object has at least one line of symmetry, then it is said to be symmetrical.
- A circle is symmetric about its diameter.

Topics Related to Symmetry of Any Circle

- Lines of Symmetry in a Parallelogram
- Axis of Symmetry Formula
- How many lines of symmetry does a regular hexagon have?
- How many lines of symmetry does an isosceles triangle have?
- How many lines of symmetry does an equilateral triangle have?
- How many lines of symmetry does a regular pentagon have?
- Lines of Symmetry in a Regular Octagon

- Example 1: Kristine told her friends that a chord of a circle can be a line of symmetry of a circle. Is she right? Solution: The diameter is the line of symmetry for a circle. The diameter is the biggest chord of the circle. Hence a chord can be the line of symmetry of a circle only if it is a diameter. Therefore, Kristine is right.
- Example 2: Determine the number of lines of symmetry for the figure given below. Solution: We know that a circle has infinite lines of symmetry but as per the given figure, a circle has been inscribed in a square. A square has 4 lines of symmetry. Therefore, the given figure has 4 lines of symmetry.

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### Does a circle have 0 or 1 side?

Mathematically a circle does not have any sides. It has a single curved line. For it to have sides those surfaces must really be straight.

#### Does a circle have more than 2 lines of symmetry?

Look at the shapes below. The symmetry of the shape on the left and its relationship to the shape on the right can be thought of in two ways:

Fold the left-hand shape along the central line. Then one side lies exactly on top of the other, and gives the shape on the right. Imagine a mirror placed along the central dotted line. The reflection in the mirror gives the other half of the shape.

This type of symmetry is called line symmetry, Any isosceles triangle has line symmetry. The dashed lines represent lines of symmetry, and each shape is said to be symmetrical about this line. The following all have line symmetry: A shape can have more than one line of symmetry. Thus a rectangle has two lines of symmetry, an equilateral triangle has three lines of symmetry, and a square has four. A circle has an infinite number of lines of symmetry since it can be folded about any diameter. Only eight of the possible lines of symmetry are indicated below. Some shapes, such as a scalene triangle, have no lines of symmetry – it is not possible to fold the shape about a line so that the two halves fit exactly on top of one another.

## Does a circle have 4 lines of symmetry?

A circle has an infinite number of lines of symmetry since any straight line passing through the centre of the circle will be a line of symmetry.

### Does a circle have 3 types of symmetry?

When considering all the lines of symmetry in a circle, we simply take all of its diameters which is infinitely many. Symmetry comes in two forms: reflectional and radial. Reflectional symmetry is symmetry across a line of symmetry; radial symmetry is symmetry about a center point.

## Is a circle 1 line?

Euclid’s definition – A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.

#### Does a circle have one line of symmetry?

Solution –

- Lisa is correct. If we fold the circle over the line she has drawn then the parts of the circle on each side of the line match up.
- Brad is also correct. If we fold the circle over the line he has drawn then the parts of the circle on each side of the line match up.
- If we fold the circle over any line through the center $O$, then the parts of the circle on each side of the line will match up. One way to create such a line is to pick a point on the top half of the circle and draw the line through that point and the center $O$. Just like there are an infinite number of points on a line (if you pick any two points, there is always another one in between them) there are an infinite number of points on the top half of the circle. Each of these points can be used to draw a line of symmetry. Since there are an infinite number of lines through the center, the circle has an infinite number of lines of symmetry.
- When the circle is folded over a line of symmetry, the parts of the circle on each side of the line match up. This means that the parts of the circle on each side of the line must have the same area. So a line of symmetry divides the circle into two parts with equal area.
- A line of symmetry for the circle must cut the circle into two parts with equal area. Below is a picture of two lines not containing $O$: Note that in each case, for a line $L$ through the circle that does not contain the center $O$, the part of the circle on the side of $L$ that contains $O$ is larger than the part of the circle on the side of $L$ which does not contain $O$. Hence these lines cannot be lines of symmetry as any line of symmetry would cut the circle in half.

## Can a circle be 1d?

A circle is one-dimensional, in the sense that it only takes one number to give the location of a point on the circle, once we have a starting point and a direction of travel along the circle.

#### Is A circle infinite?

Answer and Explanation: A circle is defined in mathematics as a type of line which is composed of infinite number of points that are equidistant from a given point. The distance from the center to any of the points along this line is called the radius.

## Why is a circle more symmetrical?

The most symmetric shape – A circle has infinitely many lines of symmetry: any diameter lies on a line of symmetry through the center of the circle. Any rotation of any amount around the center of the circle also leaves the circle unchanged.

#### What are the 4 types of symmetry?

Symmetry is said to exist if an object or figure looks the same under a transformation. Types of symmetries are rotational symmetry, reflection symmetry, translation symmetry, and glide reflection symmetry.

#### What shape has only 3 lines of symmetry?

Yes, an equilateral triangle has exactly three lines of symmetry.

#### What shape has 4 planes of symmetry?

Now, we have established that there are four planes of symmetry in a square pyramid.

#### What is the 8 symmetry property of a circle?

Defining a Circle: Circle is an eight-way symmetric figure. The shape of circle is the same in all quadrants. In each quadrant, there are two octants. If the calculation of the point of one octant is done, then the other seven points can be calculated easily by using the concept of eight-way symmetry. So we will calculate only 45°arc. From which the whole circle can be determined easily.

- If we want to display circle on screen then the putpixel function is used for eight points as shown below:
- putpixel (x, y, color) putpixel (x, -y, color) putpixel (-x, y, color) putpixel (-x, -y, color) putpixel (y, x, color) putpixel (y, -x, color) putpixel (-y, x, color)
- putpixel (-y, -x, color)
- Example: Let we determine a point (2, 7) of the circle then other points will be (2, -7), (-2, -7), (-2, 7), (7, 2), (-7, 2), (-7, -2), (7, -2)
- These seven points are calculated by using the property of reflection. The reflection is accomplished in the following way:
- The reflection is accomplished by reversing x, y co-ordinates.

There are two standards methods of mathematically defining a circle centered at the origin.

- Defining a circle using Polynomial Method
- Defining a circle using Polar Co-ordinates

Next Topic : Defining a Circle:

## What has 4 sides of symmetry?

Lines of Symmetry in a Square – In a square, there are four lines of symmetry, each of which divides it into two identical parts. The symmetry lines of a square are both its diagonals and the lines joining the midpoints of its opposite sides (bisectors).

#### What shape has 7 symmetries?

Heptagon symmetry A regular heptagon has 7 lines of symmetry and a rotational symmetry of order 7, meaning that it can be rotated in such a way that it will look the same as the original shape 7 times in 360°.

#### Do all circle have rotational symmetry?

Rotational symmetry in circles – A regular hexagon has an order of rotation of 6 6, an octagon has an order of rotation of 8 8, and a dodecagon has an order of rotation of 12 12, But what about a circle? A circle can be rotated around its centre and the shape will remain identical as the radius is the same for every point on the circumference of the circle.

## Does a circle have origin symmetry?

With respect to the origin. Solution: This circle relation has symmetry with respect to the y-axis, x-axis, and the origin. It also has reflectional symmetry over any line passing through the origin and rotational symmetry through any angle with the origin as a fixed point.

### Does a circle have point symmetry?

What shapes have a point symmetry? Any shape that has a central point that divides it into two sides, with all points on one side the same distance from all points on the other side. Some common examples are rectangles, squares, and circles.

### Does a circle have origin symmetry?

With respect to the origin. Solution: This circle relation has symmetry with respect to the y-axis, x-axis, and the origin. It also has reflectional symmetry over any line passing through the origin and rotational symmetry through any angle with the origin as a fixed point.

#### Does a circle have 360 rotational symmetry?

Rotation symmetry occurs when a shape can be rotated less than 360° and still look the same. There are three ways to name rotation symmetry: order, fraction of a turn, and angle. A circle has infinite rotation symmetry, as it can be rotated around its center through any angle and still fit onto itself.