Let's consider polygons with up to 6 sides and classify them as regular or irregular based on whether all sides are congruent or not.

1. Triangle (3 sides)

• Regular Example: Equilateral Triangle
  • All Sides Congruent: Yes, all three sides are equal.
  • All Angles Equal: Yes, each angle is 60°.
• Irregular Example: Scalene Triangle
  • All Sides Congruent: No, all sides have different lengths.
  • All Angles Equal: No, all angles are different.

2. Quadrilateral (4 sides)

• Regular Example: Square
  • All Sides Congruent: Yes, all four sides are equal.
  • All Angles Equal: Yes, each angle is 90°.
• Irregular Example: Rectangle
  • All Sides Congruent: No, opposite sides are equal, but adjacent sides are not.
  • All Angles Equal: Yes, each angle is 90°.

3. Pentagon (5 sides)

• Regular Example: Regular Pentagon
  • All Sides Congruent: Yes, all five sides are equal.
  • All Angles Equal: Yes, each interior angle is 108°.
• Irregular Example: Irregular Pentagon
  • All Sides Congruent: No, sides have different lengths.
  • All Angles Equal: No, angles are different.

4. Hexagon (6 sides)

• Regular Example: Regular Hexagon
  • All Sides Congruent: Yes, all six sides are equal.
  • All Angles Equal: Yes, each interior angle is 120°.
• Irregular Example: Irregular Hexagon
  • All Sides Congruent: No, sides have different lengths.
  • All Angles Equal: No, angles are different.

Would you like more details or have any questions?

Here are five related questions for further exploration:

1. What is the formula to calculate the sum of interior angles in an $n$-sided polygon?
2. How can you determine the area of a regular hexagon?
3. What are the properties of a regular vs. irregular quadrilateral?
4. How does the perimeter change in regular vs. irregular polygons?
5. Can a pentagon be both irregular and have all sides congruent?

Tip: When working with polygons, remember that the sum of the interior angles can be found using the formula $(n-2) \times 180^\circ$, where $n$ is the number of sides.