Chapter 11, Problem 5SGR

To determine

To state: Whether the statement “A segment drawn perpendicular to a side of a regular polygon is called an apothem of the polygon” is true or false.

Answer to Problem 5SGR

The statement is false.

Explanation of Solution

Given information:

The given statement is “A segment drawn perpendicular to a side of a regular polygon is called an apothem of the polygon”.

A polygon with equal sides and are equiangular is called a regular polygon.

For example, consider a square with center O is inscribed in a circle as shown in the Figure (1).

  

Figure (1)

From the figure, the segment OA drawn perpendicular to the side of the square from the center is called the apothem.

Hence, in general, a segment drawn from the center of a regular polygon perpendicular to the side of the polygon is an apothem.

In case of an equilateral triangle, the line segment from the vertex of a triangle drawn perpendicular to the side is the altitude of the triangle.

Thus, a segment drawn perpendicular to a side of a regular polygon is not an apothem of the polygon

Therefore, the correct statement is “A segment drawn from the center of a regular polygon perpendicular to the side of the polygon is an apothem”.