Polygons are closed, two-dimensional shapes formed by connecting straight line segments. The points where the segments meet are called vertices, and the segments themselves are called sides.
Circles and ovals are not polygons because they contain curved lines. All polygons have angles where their sides meet.
A triangle is a polygon with exactly three sides and three angles. The sum of all interior angles in any triangle always equals 180 degrees.
Triangles are the only polygons that are always rigid structures, meaning they don't change shape when pressure is applied to their sides.
A quadrilateral is a polygon with exactly four sides and four angles. The sum of all interior angles in any quadrilateral always equals 360 degrees.
Squares are special types of rectangles, and rectangles are special types of parallelograms. Understanding these relationships helps classify quadrilaterals correctly.
Pentagons have five sides, while hexagons have six sides. These polygons appear frequently in nature and human-made objects.
Regular hexagons fit together perfectly without gaps, which is why honeycombs have this shape. This efficient pattern is called tessellation.
Polygons continue with specific names as the number of sides increases. All regular polygons have equal side lengths and equal angle measures.
To find the sum of interior angles for any polygon, use the formula: (number of sides - 2) × 180 degrees.
Polygons are classified as either regular or irregular based on their side lengths and angle measures.
Most polygons in the real world are irregular. Regular polygons have special mathematical properties that make them useful in design and construction.
Polygons are classified as convex or concave based on the measure of their interior angles and the shape's overall structure.
An easy way to remember: convex polygons look like they've been "pushed out" while concave polygons have at least one "cave" or indentation. All regular polygons are convex.