Polygons
Grade 4 students learn to identify and define polygons in Saxon Math Intermediate 4. A polygon is a flat, closed shape made entirely of straight line segments. The word comes from the Greek poly meaning many and gon meaning angle. To qualify as a polygon, a shape must be two-dimensional, have only straight sides, and be fully closed with all sides connecting at endpoints. A circle is not a polygon because its boundary is curved. A triangle with an open gap is also not a polygon. This Chapter 7 skill establishes fundamental geometric vocabulary for classifying and discussing two-dimensional shapes.
Key Concepts
New Concept Polygons are closed, flat shapes formed by line segments.
What’s next Next, you’ll learn to identify and name different polygons, from triangles to decagons, based on their number of sides.
Common Questions
What is a polygon?
A polygon is a flat, closed two-dimensional shape made entirely of straight line segments. The word polygon comes from Greek meaning many angles. Examples include triangles, squares, pentagons, and hexagons.
Why is a circle not a polygon?
A circle is not a polygon because its boundary is a curved line, not straight line segments. Polygons must have only straight sides.
What three rules must a shape follow to be a polygon?
The shape must be flat (two-dimensional). It must be made only of straight line segments with no curves. All sides must connect — the shape must be closed with no gaps or open ends.
Can a polygon have an open side?
No. A polygon must be completely closed. If one side is missing or the segments do not connect at their endpoints, the shape is not a polygon. All vertices must be properly joined.
What Saxon Math chapter covers polygons?
Polygons are covered in Saxon Math Intermediate 4, Chapter 7 (Lessons 61-70), as the foundation for studying polygon properties including sides, vertices, and types of polygons.