1. What is a Polygon? (Simple Idea)
In middle school geometry, we see many shapes made from straight line segments. Some of these shapes are called polygons. A polygon is like a closed shape made by joining straight sticks end to end.
Imagine you draw some straight line segments on paper so that:
- each segment joins exactly to the next one at its end, and
- the last segment again joins back to the first one.
If this happens and the shape is closed (no gap), then you are most likely looking at a polygon.
1.1. Closed Broken Line Idea
You can think of a polygon as a closed broken line made of straight pieces. It is called "broken" because the direction changes at the corners, and it is called "closed" because it comes back to the starting point.
Important points:
- The sides are straight line segments, not curves.
- There is no gap in the boundary.
- The sides meet only at their end points.
1.2. Examples and Non-Examples (Quick Check)
- A triangle, a rectangle, a pentagon – all are polygons.
- A circle is not a polygon because its boundary is curved.
- A shape with an open side (not fully closed) is not a polygon.
- A shape where sides cross each other in the middle is not a simple polygon.
2. Formal Definition and Basic Terms
Now let us write a neat definition that we can use in maths:
Definition: A polygon is a closed plane figure formed by a finite number of straight line segments such that each segment intersects exactly two others, one at each end point.
This definition may look long, but it captures all the important conditions needed for a shape to be a polygon.
2.1. Basic Terms in a Polygon
To talk clearly about polygons, we use some standard words:
- Side: Each straight line segment of a polygon is called a side.
- Vertex (plural: vertices): The common end point where two sides meet is called a vertex.
- Adjacent sides: Two sides that share a common vertex are called adjacent sides.
- Interior: The region or space inside the polygon is called its interior.
- Exterior: The region outside the polygon is called its exterior.
- Interior angle: The angle formed inside the polygon between two adjacent sides is called an interior angle.
2.2. How We Draw and Label a Polygon
Usually we name the vertices of a polygon using capital letters like A, B, C, D, ... and join them in order using straight line segments.
For example:
- A polygon with 4 vertices A, B, C and D can be drawn and named as ABCD. The sides are AB, BC, CD and DA.
- If a polygon has vertices P, Q, R, S, T, we can call it polygon PQRST.
When we write the name of a polygon like ABCD, we always list the vertices in order around the shape (either clockwise or anticlockwise).
3. Naming Polygons by Number of Sides
Polygons are often classified and named according to the number of sides (or vertices) they have. If a polygon has \( n \) sides, we call it an \( n \)-gon.
Here are some common names that you will use frequently:
3.1. Common Polygon Names
| Number of sides | Name of polygon | Example |
|---|---|---|
| 3 | Triangle | Shape of a simple traffic warning sign |
| 4 | Quadrilateral | Rectangle, square, kite |
| 5 | Pentagon | Some home plate designs, certain stars inside |
| 6 | Hexagon | Honeycomb cell, some floor tiles |
| 7 | Heptagon | Less common in daily life, but used in designs |
| 8 | Octagon | Stop sign in some countries |
In general, for \( n \geq 3 \), a polygon with \( n \) sides can be called an \( n \)-gon, for example:
- \( 9 \)-gon: polygon with 9 sides
- \( 10 \)-gon: polygon with 10 sides
3.2. Important Note for Your Personal Notes
Every polygon must have at least \( 3 \) sides, so the smallest possible polygon is a triangle. There is no largest polygon because we can keep increasing the number of sides \( n \). That is why using the word \( n \)-gon is very handy when writing general formulas later.
4. Polygons Around You (Everyday Examples)
Once you know the idea of a polygon, you start noticing them everywhere around you. This makes the topic feel much more natural and less like dry theory.
4.1. Spot the Polygons in Real Life
- Classroom objects: Top of your desk (usually a rectangle), notice board (often a rectangle), some windows (rectangles or squares).
- Road signs: Triangular speed warning signs, octagonal stop signs.
- Home and city: Floor tiles (squares, rectangles, sometimes hexagons), wall tiles, mirrors, photo frames.
- Nature and patterns: Honeycomb cells (hexagons), some flower patterns and geometric rangoli designs use polygons.
You can quickly sketch these shapes in your notebook and label the sides and vertices. This will make the idea of polygons feel familiar and easy to remember during exams.