lecture notes on Polygons

1. Introduction

• Welcome message from Adarsh.
• Topic: Polygons (Chapter 3).
• Importance of full attention during the lecture to succeed in exams.

2. Polygons Explained

• Definition: Closed figures made up of straight lines.
• Minimum number of lines to form a polygon: 3 (Triangle).
• Types of polygons:
  • Triangle (3 sides)
  • Quadrilateral (4 sides)
  • Pentagon (5 sides)
  • Hexagon (6 sides)
  • Heptagon (7 sides)
  • Octagon (8 sides)
  • Nonagon (9 sides)
  • Decagon (10 sides)

3. Properties of Polygons

3.1 Angles in Polygons

• Triangle: Sum of angles = 180 degrees.
• Quadrilateral: Sum of angles = 360 degrees.
• General formula for sum of angles in an n-sided polygon:
  • Sum of angles = (n - 2) * 180 degrees
• Example: For a polygon with 20 sides, the sum of angles would be 18*180 = 3240 degrees.

3.2 Diagonals in Polygons

• Formula for number of diagonals in an n-sided polygon:
  • Diagonals = n(n - 3)/2
• For example, a pentagon has 5 sides, thus it can have 5(5-3)/2 = 5 diagonals.

4. Regular Polygons

• Definition: A polygon where all sides and angles are equal.
• Example: Equilateral triangle, square, regular pentagon.
• Calculation of each angle in a regular polygon:
  • Each angle = (Sum of angles) / n

5. Conclusion

• Importance of understanding the properties and formulas related to polygons for solving mathematical problems.
• Encouragement for students to actively participate and comment during the lecture.