Let me analyze the image and interpret the text to provide a solution.### Analysis of the Question:

Case Study Information:

• Polygons are defined as closed figures made up of only line segments.
• Two polygons are provided:
  • Polygon-1: A quadrilateral.
  • Polygon-2: A pentagon.

Questions to Answer:

1. Identify the regular polygon and make a copy of it.
2. What is that polygon called?
3. Draw a triangle within it by joining the vertices of the polygon.
4. Is a rectangle a regular polygon? State the reason for your answer.

Solutions:

1. Identify the Regular Polygon and Make a Copy of It:

   • The second polygon (Polygon-2) is a regular polygon because:
     • All its sides are equal in length.
     • All its interior angles are equal.
   • This polygon is a pentagon (as mentioned in the provided answer).

2. What Is That Polygon Called?

   • The polygon in question (Polygon-2) is a pentagon.

3. Draw a Triangle Within It by Joining the Vertices of the Polygon:

   • To draw a triangle within the pentagon, any three vertices of the pentagon can be joined. For instance:
     • Connect vertices A, C, and E (or any other combination of three vertices).

4. Is a Rectangle a Regular Polygon? State Reason for Your Answer:

   • No, a rectangle is not a regular polygon because:
     • Although its opposite sides are equal, all sides are not equal.
     • Additionally, the angles are equal (90°), but the sides being unequal disqualifies it from being regular.

Would you like a detailed drawing or more clarification? Let me know! 😊

Follow-Up Questions:

1. What are the differences between regular and irregular polygons?
2. Can a pentagon be both concave and convex? How would you classify Polygon-2?
3. What formula can be used to calculate the interior angle of a regular polygon?
4. How many diagonals can be drawn from a pentagon? Explain the calculation.
5. Can a triangle ever be considered a regular polygon? Why?

Tip:

To determine if a polygon is regular, always check both equal sides and equal angles!