Classify each polygon below by the number of its sides and determine if it is equilateral, equiangular, or regular. Justify your answer.

Here are the classifications for each polygon:

1. Regular Octagon

• Number of sides: 8
• Equilateral: Yes
• Equiangular: Yes
• Regular: Yes
• Justification: All 8 sides are equal in length, and all 8 interior angles are equal in measure.

2. Equilateral Triangle

• Number of sides: 3
• Equilateral: Yes
• Equiangular: Yes
• Regular: Yes
• Justification: All three sides are equal in length, and all three interior angles measure $60^\circ$.

3. Rhombus

• Number of sides: 4
• Equilateral: Yes
• Equiangular: No
• Regular: No
• Justification: All four sides are equal in length, but the interior angles are not all equal (it has two acute and two obtuse angles).

4. Regular Pentagon

• Number of sides: 5
• Equilateral: Yes
• Equiangular: Yes
• Regular: Yes
• Justification: All five sides are equal in length, and all five interior angles measure $108^\circ$.

5. Isosceles Triangle

• Number of sides: 3
• Equilateral: No
• Equiangular: No
• Regular: No
• Justification: Only two sides are equal in length, and only the two base angles are equal in measure.

6. Rectangle

• Number of sides: 4
• Equilateral: No
• Equiangular: Yes
• Regular: No
• Justification: All four interior angles are $90^\circ$, but only opposite sides are equal in length, not all four sides.