What Is a Polygon?
A polygon is a closed, flat shape bounded entirely by straight sides. In Grade 6 Saxon Math Course 1, students verify the three conditions for a polygon: the shape must be closed (all sides connect), have only straight sides (no curves), and be two-dimensional (flat). Circles and shapes with open sides or curved boundaries are not polygons. Polygons are classified by the number of sides: 3 (triangle), 4 (quadrilateral), 5 (pentagon), 6 (hexagon), up to any number of sides.
Key Concepts
Property Polygons are closed, flat shapes with straight sides.
Examples A stop sign is a polygon because it is a closed, flat shape with 8 straight sides. A perfect circle is not a polygon because its entire edge is one continuous curve. The letter 'S' is not a polygon because it is an open shape and has curves.
Explanation Think of a polygon as a perfectly secure fence! For a shape to count, it must be completely closed with no escape gaps, it must be flat on the ground (2D), and it must be built with straight sections, not curvy ones. Any shape that breaks these rules is an imposter!
Common Questions
What three conditions must a shape satisfy to be a polygon?
1) It must be a closed shape (no gaps). 2) It must have only straight sides. 3) It must be flat (two-dimensional).
Is a circle a polygon?
No. A circle has a curved boundary, violating the straight-sides requirement.
What is a hexagon?
A polygon with six sides and six vertices.
What is the difference between a regular and an irregular polygon?
A regular polygon has all sides equal and all interior angles equal. An irregular polygon has sides or angles of different measures.
Name all polygon types from 3 to 8 sides.
3: triangle, 4: quadrilateral, 5: pentagon, 6: hexagon, 7: heptagon, 8: octagon.