Even though the concept of an infinite number of lines is fairly abstract, fourth graders can understand infinity in an informal way.
Just as there is always a fraction between any two fractions on the number line, there is always another line through the center of the circle "between" any two lines through the center of the circle.
So if you identify a certain number of lines, you can argue that there is always at least one more. This task includes an experimental GeoGebra worksheet, with the intent that instructors might use it to more interactively demonstrate the relevant content material. The file should be considered a draft version, and feedback on it in the comment section is highly encouraged, both in terms of suggestions for improvement and for ideas on using it effectively.
The file can be run via the free online application GeoGebra , or run locally if GeoGebra has been installed on a computer. 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. A line of symmetry for the circle must cut the circle into two parts with equal area. 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. 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. 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. Pranav Kanchi. Any diameter must go through the center and two points on the circle; making it cut the circle's circumference into two equal parts This makes it a line of symmetry;.
Think about the diameters of a circle; If you rotate the diameter around the center of the circle by any very small part of a fraction it becomes a different line of symmetry. Elise Molinaro. Liza Sulkin. You've reached the end. How can we improve? Fastforward Forerunner.
A circle is also 1 seconds of arc, which nullifies the arguement that degrees must equal lines of symmetry. A second is the smallest unit to measure degrees. What's A Scope? Messages: 3, Likes Received: Lines do not have width. Zendarrun Forerunner. Prosper Promethean. Theoretically, there is no circle, just a bunch of lines making the illusion of the perfect circle, maybe your teacher was trying to be a turd and was being literal. If it were lines, wouldn't that have 0 lines of symmetry?
A line drawn would be considered a bisector not a line of symmetry. You must log in or sign up to post here. Show Ignored Content. Share This Page Tweet. Your name or email address: Do you already have an account?
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