"A polygon is a plane figure made up of line segments connected to form a closed polygonal chain."
Polygons are closed shapes with three or more straight sides, and this topic covers how to classify polygons by their number of sides, how to find missing angles and side lengths of polygons, and the properties of regular polygons.
Polygon definition: A closed figure formed by three or more line segments is called a polygon.
Regular polygon: A polygon that has all sides and angles equal.
Irregular polygon: A polygon that has sides and angles of different lengths and measures.
Convex polygon: A polygon whose interior angles are all less than 180 degrees.
Concave polygon: A polygon with at least one interior angle greater than 180 degrees.
Exterior angle theorem: The measure of an exterior angle of a polygon is equal to the sum of the measures of its two remote interior angles.
Interior angle theorem: The sum of the interior angles of a polygon is equal to (n-2) x 180 degrees, where n is the number of sides of the polygon.
Angle measures of polygons: The measure of each interior angle of a regular polygon is found by dividing the sum of the interior angles by the number of sides.
Perimeter of polygons: The perimeter of a polygon is the sum of the lengths of its sides.
Area of polygons: The area of polygons can be found by dividing the polygon into simpler shapes and using their formulas.
Congruent polygons: Two polygons are said to be congruent if they have the same size and shape.
Similar polygons: Two polygons are said to be similar if they have the same shape but different sizes.
Polygons in the real world: Polygons can be found in many real-world applications such as buildings, bridges, and art.
Triangle: A polygon with three sides and three angles.
Quadrilateral: A polygon with four sides and four angles.
Pentagon: A polygon with five sides and five angles.
Hexagon: A polygon with six sides and six angles.
Heptagon: A polygon with seven sides and seven angles.
Octagon: A polygon with eight sides and eight angles.
Nonagon: A polygon with nine sides and nine angles.
Decagon: A polygon with ten sides and ten angles.
Hendecagon: A polygon with eleven sides and eleven angles.
Dodecagon: A polygon with twelve sides and twelve angles.
Tridecagon: A polygon with thirteen sides and thirteen angles.
Tetradecagon: A polygon with fourteen sides and fourteen angles.
Pentadecagon: A polygon with fifteen sides and fifteen angles.
Hexadecagon: A polygon with sixteen sides and sixteen angles.
Heptadecagon: A polygon with seventeen sides and seventeen angles.
Octadecagon: A polygon with eighteen sides and eighteen angles.
Enneadecagon: A polygon with nineteen sides and nineteen angles.
Icosagon: A polygon with twenty sides and twenty angles.
N-gon: A polygon with any number of sides greater than three.
"The segments of a closed polygonal chain are called its edges or sides."
"The points where two edges meet are the polygon's vertices or corners."
"An n-gon is a polygon with n sides; for example, a triangle is a 3-gon."
"A simple polygon is one which does not intersect itself."
"The only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain."
"A simple polygon is the boundary of a region of the plane that is called a solid polygon."
"The interior of a solid polygon is its body, also known as a polygonal region or polygonal area."
"Yes, a polygonal chain may cross over itself, creating star polygons and other self-intersecting polygons."
"Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skew polygon), even when the chain does not lie in a single plane."
"A polygon is a 2-dimensional example of the more general polytope in any number of dimensions."
"Yes, there are many more generalizations of polygons defined for different purposes."
"A polygon is a plane figure made up of line segments connected to form a closed polygonal chain."
"A triangle is a 3-gon."
"The only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain."
"The interior of a solid polygon is its body, also known as a polygonal region or polygonal area."
"Yes, a polygonal chain may cross over itself, creating star polygons and other self-intersecting polygons."
"Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skew polygon), even when the chain does not lie in a single plane."
"A polygon is a 2-dimensional example of the more general polytope in any number of dimensions."
"Yes, there are many generalizations of polygons defined for different purposes."