which of the following is not a polygon
The correct answer and explanation is:
To correctly identify which of the following is not a polygon, we must first understand the definition of a polygon. A polygon is a closed, two-dimensional shape made up of straight line segments connected end-to-end. These line segments are called sides, and the points where the sides meet are called vertices. A polygon must have at least three sides and must be completely closed. Examples include triangles, rectangles, pentagons, and hexagons.
If given options are like:
a. Triangle
b. Circle
c. Pentagon
d. Square
The correct answer is: b. Circle
Explanation:
A circle is not a polygon because it does not consist of straight line segments. Instead, a circle is formed by a continuous curved line where all points are equidistant from the center. Unlike a polygon, it does not have sides or vertices.
A triangle, square, and pentagon are all polygons.
- A triangle has 3 straight sides and 3 angles.
- A square has 4 straight sides of equal length and 4 right angles.
- A pentagon has 5 straight sides and 5 angles.
What distinguishes polygons is that they are made of straight lines and form a closed shape. In contrast, any shape that involves a curve, open ends, or non-linear edges cannot be classified as a polygon.
Identifying non-polygon shapes is crucial in geometry because many principles, such as area formulas and internal angle calculations, apply only to polygons. By understanding that a circle is not composed of straight lines and lacks the features of a polygon, it becomes clear why it does not qualify as one. Thus, in the given choices, the circle is not a polygon.