Assertion (A): A Circle Has Infinitely Many Lines Of Symmetry. Reason (R): A Circle Has Only One Diameters. (A) Both A And R True And R Is The Correct Explanation For A (B) Both A And R True And R Is Not The Correct Explanation For A (C) A Is True But

Mar 10, 2025 by ADMIN 252 views

Understanding the Assertion and Reason

Introduction

In geometry, a circle is a fundamental shape that has several unique properties. One of the key characteristics of a circle is its symmetry. In this article, we will explore the assertion that a circle has infinitely many lines of symmetry and the reason provided for this assertion, which states that a circle has only one diameter. We will examine the validity of the reason and determine whether it is the correct explanation for the assertion.

The Assertion: A Circle Has Infinitely Many Lines of Symmetry

A circle is a continuous curved shape that is perfectly round and has no beginning or end. One of the key properties of a circle is its symmetry. Symmetry in a circle refers to the ability of the circle to look the same from different angles. In other words, if you rotate a circle by any angle, it will still look the same. This property of symmetry is a fundamental characteristic of a circle and is a key reason why circles are so important in mathematics and science.

The assertion that a circle has infinitely many lines of symmetry is a statement that is often made in geometry. This assertion is based on the fact that a circle can be rotated by any angle and still look the same. In other words, a circle has an infinite number of rotational symmetries. This means that if you rotate a circle by any angle, it will still look the same. This property of symmetry is a fundamental characteristic of a circle and is a key reason why circles are so important in mathematics and science.

The Reason: A Circle Has Only One Diameter

The reason provided for the assertion that a circle has infinitely many lines of symmetry is that a circle has only one diameter. A diameter is a line that passes through the center of a circle and connects two points on the circle. The reason provided is that a circle has only one diameter, which is the longest possible line that can be drawn through the center of the circle.

However, this reason is not a correct explanation for the assertion that a circle has infinitely many lines of symmetry. The reason provided is based on the fact that a circle has only one diameter, but this does not explain why a circle has infinitely many lines of symmetry. In fact, the reason provided is not even related to the assertion that a circle has infinitely many lines of symmetry.

Analyzing the Assertion and Reason

To determine whether the reason provided is a correct explanation for the assertion, we need to analyze the assertion and reason separately. The assertion that a circle has infinitely many lines of symmetry is a statement that is based on the fact that a circle can be rotated by any angle and still look the same. This property of symmetry is a fundamental characteristic of a circle and is a key reason why circles are so important in mathematics and science.

On the other hand, the reason provided is that a circle has only one diameter. This reason is not a correct explanation for the assertion that a circle has infinitely many lines of symmetry. In fact, the reason provided is not even related to the assertion that a circle has infinitely many lines of symmetry.

Conclusion

In conclusion, the assertion that a circle has infinitely many lines of symmetry is a statement that is based on the fact that a circle can be rotated by any angle and still look the same. This property of symmetry is a fundamental characteristic of a circle and is a key reason why circles are so important in mathematics and science.

The reason provided for the assertion that a circle has infinitely many lines of symmetry is that a circle has only one diameter. However, this reason is not a correct explanation for the assertion. In fact, the reason provided is not even related to the assertion that a circle has infinitely many lines of symmetry.

Therefore, the correct answer is (B) Both A and R true and R is not the correct explanation for A.

References

Geometry: A Comprehensive Introduction by Dan Pedoe
The Elements of Geometry by Euclid
A History of Mathematics by Carl B. Boyer