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.

Explore classifications of polygons with up to 6 sides, distinguishing between regular and irregular examples. This problem covers fundamental geometric concepts such as polygon classifications and the formula for calculating the sum of interior angles. Suitable for Grades 6-8.

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