Which polygon or polygons are regular? (Classifying Polygons Practice)
what polygons are regular and how to identify them and same for irregular?
Regular polygons are polygons that have equal lengths for all sides and equal angles for all vertices. Here are some examples of regular polygons:
- Equilateral Triangle: All sides are equal and all angles are 60 degrees.
- Square: All sides are equal and all angles are 90 degrees.
- Regular Pentagon: All sides are equal and all angles are 108 degrees.
- Regular Hexagon: All sides are equal and all angles are 120 degrees.
- Regular Octagon: All sides are equal and all angles are 135 degrees.
On the other hand, irregular polygons are polygons that do not have equal sides or angles. Here are some examples of irregular polygons:
- Scalene Triangle: No sides or angles are equal.
- Rectangle: Opposite sides are of equal length but not all sides and angles.
- Quadrilateral: A polygon with four sides and angles, the sides may have different lengths and angles may be unequal.
- Trapezoid: Only two opposite sides are parallel.
- Irregular Pentagon: Any pentagon that does not have equal sides and angles.
what about a rhombus
A rhombus is a special type of quadrilateral that has a different property than other irregular quadrilaterals. A rhombus has all sides equal in length, but the angles between the sides may not be equal. Even though a rhombus doesn't have equal angles, it is still considered a regular polygon because of its side lengths. Therefore, a rhombus is a regular polygon.
To determine which polygons are regular, we need to understand what it means for a polygon to be regular. A regular polygon is a polygon that has equal side lengths and equal angle measures for each of its interior angles.
To classify polygons as regular or not, we can examine the properties of each polygon.
1. Triangle: A triangle can be regular if it meets the criteria of having equal side lengths and equal angle measures. Equilateral triangles have three equal sides and three equal interior angles of 60 degrees each. Therefore, an equilateral triangle is a regular polygon.
2. Quadrilateral: A quadrilateral can be regular if it meets the criteria of having equal side lengths and equal angle measures. There are special types of quadrilaterals that are regular, such as a square. A square has four equal sides and four right angles, making it a regular polygon.
3. Pentagon: A regular pentagon has five equal sides and five equal interior angles, each measuring 108 degrees. Therefore, a regular pentagon is a regular polygon.
4. Hexagon: A hexagon can be regular or irregular. A regular hexagon has six equal sides and six equal interior angles, each measuring 120 degrees. However, if the side lengths or angle measures vary, it is an irregular hexagon. Therefore, a hexagon may or may not be regular.
5. Heptagon (or Septagon): A regular heptagon has seven equal sides and seven equal interior angles, each measuring 128.57 degrees. Therefore, a regular heptagon is a regular polygon.
6. Octagon: A regular octagon has eight equal sides and eight equal interior angles, each measuring 135 degrees. Therefore, a regular octagon is a regular polygon.
In summary:
- Equilateral triangles, squares, regular pentagons, regular heptagons, and regular octagons are considered regular polygons.
- Hexagons can be regular or irregular depending on the side lengths and angle measures.
Remember that a regular polygon has equal side lengths and equal angle measures for all its interior angles. By examining the sides and angles of each polygon, we can determine if it is regular or not.