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Use polygon vocabulary

A polygon is a closed, two-dimensional figure made of straight line segments, with sides, vertices, and interior angles; figures with curved boundaries, open boundaries, or overlapping sides are not polygons. The learner names and classifies common polygons by number of sides—such as triangles, quadrilaterals, pentagons, and hexagons—and distinguishes regular from irregular and, where relevant, convex from concave figures; formal proofs and generalized polygon theory are beyond this scope.

Detailed Explanation: Use polygon vocabulary

A polygon is a closed, flat figure made only of straight line segments.

  • Sides are the straight segments.
  • Vertices are the corners where two sides meet.
  • Interior angles are the angles inside the figure.

To classify a polygon:

  1. Check that the figure is closed.
  2. Check that every boundary part is straight.
  3. Count the sides (and vertices).
  4. Use the number of sides to name it.
  5. Decide whether it is regular or irregular.
  6. If needed, decide whether it is convex or concave.

Worked example

Imagine a closed figure with six straight sides. One part of the boundary makes an inward “dent,” and the sides are different lengths.

Step 1: Is it a polygon?
Yes. The figure is closed, and all of its sides are straight.

Step 2: Count the sides.
Count each straight segment around the outside:

6 sides6 \text{ sides}

There are also 66 vertices and 66 interior angles.

Step 3: Name the polygon.
A polygon with 66 sides is a hexagon.

Step 4: Decide whether it is regular or irregular.
The sides are different lengths, so the figure is irregular. A regular hexagon would have all sides and all interior angles equal.

Step 5: Decide whether it is convex or concave.
The inward dent creates an interior angle that points inward. Therefore, the hexagon is concave.

So, the figure is an irregular, concave hexagon.

Learn by doing: Use polygon vocabulary

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Classifying Polygons by Sides (Real World)


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