Question

State the following as True or False
A regular octagon has 10 lines of symmetry.
A. True
B. False

Answer 1

Hint: This problem involves the concept of regular figure and thorough knowledge of the number of sides according to the named figure. So, the idea of naming a figure based on its number of sides is a must for solving this problem.

Complete step-by-step answer:

In mathematics a field dedicated for study of shapes is called geometry. The field of “Geometry” emphasizes on the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues. It is concerned with the questions of shape, size, relative position of figures, and the properties of space.
A person who analyses the geometrical figure is called a geometer. Some of the popular geometers include Euclid, Pythagoras etc.
A figure having equal sides is called a regular figure. In other words, a closed figure whose all sides and included angles of the sides are equal satisfies all the necessary and sufficient conditions for becoming a regular figure. For example, the most commonly used regular figure is square.
According to our question we have a regular octagon.
An octagon is a closed figure of 8 sides. A regular octagon is a closed figure of equal 8 sides.
For a closed figure of n sides, the number of lines of symmetry is equivalent to n. Line of symmetry is that line about which a figure seems to be symmetrical or a mirror image of the figure.
So, we conclude that a regular octagon has 8 lines of symmetry. This proves that the statement of the question is false.
Hence, the correct option is (b).

Note: The key step is the knowledge of regular figures and naming of figures according to the number of sides. For simplicity, the prefixes are a great way to memorize these names, such as tri- for 3, quad- for 4, pent- for 5, hex- for 6, and so on. Similarly, in this question, the prefix is oct- which is the prefix for 8 and not 10.