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Symmetry of Any Circle
If we fold a circle over any of its diameters, then the parts of the circle on each side of the diameter will match up depicting that the parts of the circle on each side of the diameter must have the same area. Thus, any diameter of a circle can be considered as a line of symmetry for the circle. We can check whether an object is symmetrical or not if we are able to divide an object into two symmetrical parts by drawing a line. If a line divides an object into two symmetrical parts, then the object is said to be symmetrical. An object can have zero lines of symmetry or it can have infinite lines of symmetry.
|What is Symmetry of Any Circle?
|Solved Examples on Symmetry of Any Circle
|Practice Questions on Symmetry of Any Circle
|FAQs on Symmetry of Any Circle
What is Symmetry of any Circle?
We know that the diameter of a circle is a line passing through its center. So, the diameter acts as a line of symmetry dividing the circle into two parts with equal area. There is an infinite number of lines passing through the center, thus a circle has an infinite number of lines of symmetry.
Symmetry in a Circle
A circle is symmetrical about any of its diameter. By symmetrical, we mean that the circle can be divided into two congruent parts by any of its diameter. Look at the figure given below! The circle with center O is symmetrical about its diameter AB.
When a figure is rotated around its center point and still appears exactly as it was before the rotation, then it is said to have rotational symmetry. A circle has rotational symmetry. The order of the symmetry in a circle is infinite. That means if we rotate the circle by any degree of angle along its diameter, it will always be symmetrical around the diameter.
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?
- 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
Solved Examples on Symmetry of Any Circle
Example 1: Kristine told her friends that a chord of a circle can be a line of symmetry of a circle. Is she right?
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.
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.
FAQs on Symmetry of Any Circle
Can a Circle Be Symmetrical?
Yes, a circle is symmetric about its diameter and a circle can have infinite lines of symmetry.
Which Shape has Only One Line of Symmetry?
An isosceles triangle is symmetric along the bisector of the vertical angle and thus has one line of symmetry.
Where Can you Find Symmetry in Nature?
In real-time, we come across many symmetrical objects around us, such as a butterfly is symmetrical and the Taj Mahal is a perfect example of symmetry.
Is the Circle Symmetric to the Origin?
On drawing an axis of symmetry passing through the origin, the circle shows symmetry about that axis. Thus, a circle is symmetric about the origin
What is the Axis of Symmetry of a Circle?
A circle has infinitely many lines of symmetry. Any line through its center (that is, any diameter) is an axis of symmetry. The x-axis is just the line y = 0, and the y-axis is just the line x = 0.
Does a circle have 360 lines of symmetry?
A circle is comprised of 360 degrees. To show or prove the multiple lines of symmetry, just draw an axis point (the center of the circle) and then rotate it by a particular angle. A circle has an infinite symmetry that is due to the fact we can draw an infinite number of diameters on the circle and that represents the line of symmetry.