Which of the following shapes is a regular polygon?a)Rectangleb)Square...
A square is a regular polygon because it has equal-length sides and equal angles. The other shapes do not meet both criteria.
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Which of the following shapes is a regular polygon?a)Rectangleb)Square...
Understanding Regular Polygons
A regular polygon is defined as a shape with all sides and angles equal. Let's analyze the given options to determine which one qualifies as a regular polygon.
Option A: Rectangle
- A rectangle has opposite sides that are equal in length, but adjacent sides are not.
- The angles in a rectangle are equal (90 degrees), but the sides are not uniform.
Option B: Square
- A square has four equal sides and four equal angles (90 degrees).
- This uniformity in both sides and angles makes the square a regular polygon.
Option C: Circle
- While a circle is symmetrical and has all points equidistant from the center, it does not have sides or angles.
- Therefore, it does not meet the criteria for a polygon, regular or irregular.
Option D: Ellipse
- An ellipse is also a smooth curve that does not consist of straight sides or angles.
- Like the circle, it lacks the properties required to be classified as a polygon.
Conclusion
- Among the options, the only shape that is a regular polygon is the square (Option B).
- It exhibits the necessary properties of being both equilateral (equal sides) and equiangular (equal angles).
In summary, the square is the correct answer because it fulfills all the criteria of a regular polygon, making it unique among the given options.