CONVEX POLYGON
Definition Of Convex Polygon
A polygon is convex if any line segment joining any two points on it stays inside the polygon itself.
More About Convex Polygon
In a convex polygon, a rubber band fits snugly without leaving any gap.
The measure of the internal angles of a convex polygon is always less than 180°.
Video Examples:Convex Polygon
Example of Convex Polygon
The above figures shown are convex polygons.
Solved Example on Convex Polygon
Ques: Count the number of convex polygons among the given figures.
Choices:
A. 1
B. 2
C. 3
D. 4
Correct Answer: C
Solution:
Step 1: Any two points in the interior of a convex polygon can be connected with a
line segment that does not cut a side of the polygon.
Step 2: If a line is drawn through each given polygon, it does not cut the sides of the Figures 1, 2, and 4.
Step 3: Therefore, there are 3 convex polygons among the given figures.
Quick Summary
- A convex polygon has all interior angles less than 180 degrees.
- A rubber band placed around a convex polygon will fit snugly.
🍎 Teacher Insights
Use visual aids and real-world examples to demonstrate the concept of convexity. Have students draw various polygons and determine whether they are convex or concave.🎓 Prerequisites
- Basic understanding of polygons
- Knowledge of line segments
- Familiarity with angles
Check Your Knowledge
Q1: Which of the following polygons is convex?
Q2: Which statement is true about convex polygons?
Frequently Asked Questions
Q: What is the difference between a convex and a concave polygon?
A: In a convex polygon, all interior angles are less than 180 degrees. In a concave polygon, at least one interior angle is greater than 180 degrees.
Q: Is a regular polygon always convex?
A: Yes, a regular polygon (all sides and angles equal) is always convex.