InterMath Dictionary
Polygon
Check for Understanding
Enter each answer in the left column, then press tab
Circumscribed Circles and Polygons in Your World
These quilts show circumscribed circles and polygons.
External Links to Extend Basic Understanding
More Definitions: Visit another online dictionary to clarify your understanding. Perimeter Problems: Here you can find some practice problems with perimeter. More Perimeter Problems: Here you can find more practice problems with perimeter. Download: Download a game to practice with perimeter (note: Mac only).
Related Investigations on InterMath to Challenge Teachers
Diagonals in a Polygon: Consider the number of diagonals in a triangle, quadrilateral, pentagon, hexagon, heptagon, and octagon. Round Robin Tournament: Use the sides and diagonals in a regular polygon to create a round robin tournament Apothem and Area: Explore the relationship between the apothem, perimeter, and area of a regular polygon. Surrounding Squares: Find a method that will construct a square that has the same area as the area of a given circle. Inscribed in a Triangle: Construct a circle inscribed in a triangle so that it will always remain inscribed in the triangle.
Did you know?
All polygons are simple, closed polygonal curves. The word "polygon" derives from the Greek words poly (many) and gonu (knee). So a polygon is a thing with many knees!
Regular Polygons in Your World
The eight-sided polygon picture in the tile below is regular. So are the six-sided polygons used to make the quilt.
How would you describe me? Give the most accurate response.
Choose one curve closed curve simple closed curve polygonal curve polygonal closed curve simple polygonal closed curve
Further Investigations of Polygons: Investigate other features of regular polygons. Polygons With LOTS of Sides: How many sides does a polygon have to have before it turns into a circle? (or does it?)
Vertex Angles in a Regular Polygon: Investigate how the vertex angle of a regular polygon relates to its number of sides. Sum of Angles in a Polygon: Explore the relationship between the number of sides of a polygon and the sum of its interior angles. Sum of Exterior Angles: Determine the sum of the exterior angles in any polygon. Medial Polygons: Investigate the characteristics of a polygon that is generated by connecting the midpoints of consecutive sides of a polygon. Apothem and Area: Explore the relationship between the apothem, perimeter, and area of a regular polygon.
Top of Page
The line segments that form a polygon are called the sides of the polygon. A point where two sides meet is a vertex (plural form is vertices). Any two sides determine an interior angle of the polygon; an exterior angle is formed by a side and an adjacent side extended.
Given Polygon ABCD then its:
Sides are AB, BC, CD, CE, and EA.
Vertices are A, B, C, D, and E.
Interior angles: ex. angle BCD (green angle)
Exterior angles: ex. angle EDJ (yellow angle)
There are three parts to a polygon: the interior (green region), the exterior (yellow region), and the polygon itself (black region). The polygon and its interior make up a polygonal region.
Examples of Adjacent Sides
In triangle on the left, sides d and f are considered adjacent sides of the triangle ABC since they share the common vertex B. Can you ideniify other sides that are adjacent?
In the square on the right, sides f and g are considered adjacent sides of the square ABCD since they share the common vertex C.
Non-Examples of Adjacent Sides In the square above, sides f and h are not adjacent sides since they do not share a common vertex. Likewise, sides e and g are not adjacent sides of the square.
Use quadrilateral ABCD to answer the following questions:
Enter the answer to part (a) in the left column, then press tab. Answer part (b) by making a selection from the menu.
Graded
Response
Further Investigations of Polygons: Investigate other features of regular polygons. Flatland by Edwin A. Abbott: Read a classic book that imagines a two dimensional world, online!
N-Sided Circle?: Compare the perimeters of polygons to the circumference of the circle. Constructing quadrilaterals 1: Given two parallel lines, form various quadrilaterals. Integral sides: Explore area and perimeter of quadrilaterals whose sides have integral length. Double Trouble: Modify components of a square and determine if a proportional relationship exists. To Be or Not to Be: Determine the necessary conditions to create a triangle.
An angle is an exterior angle of a polygon if and only if it forms a linear pair with one of the angles of the polygon.
An interior angle of a polygon is formed by two consecutive sides of a polygon. You will sometimes see an interior angle called a vertex angle.
Answer the following questions about interior and exterior angles related to triangle BCE.
Graded Response
Investigate Interior Angles of Polygons: What do all the interior angles of a polygon add up to? Investigate Exterior Angles of Polygons: What do all the exterior angles of a polygon add up to?
Remotely Interior: Compare exterior angles with remote interior angles. Sum of Angles in a Polygon: Explore the relationship between the number of sides of a polygon and the sum of its interior angles. Sum of Exterior Angles: Determine the sum of the exterior angles in any polygon. Interior angles: Explore the sum of interior angles of a quadrilateral.
Convex or Concave Polygons in Your World
Here are some examples of convex and concave polygons.
Ask Dr. Math: Dr. Math discusses convex and concave polygons. Explore Convex Polygons: Investigate the relationships among polygons and their exterior and interior angles.
Sum of Angles in a Polygon: Explore the relationship between the number of sides of a polygon and the sum of its interior angles. Sum of Exterior Angles: Determine the sum of the exterior angles in any polygon. Medial Polygons: Investigate the characteristics of a polygon that is generated by connecting the midpoints of consecutive sides of a polygon. Quadrilaterals inscribed inside quadrilaterals: Explore properties of quadrilaterals constructed using the midpoint of given quadrilaterals. Quadrilaterals inscribed inside polygons: How many quadrilaterals can be constructed using the vertices of polygons.
Any side of a triangle can serve as a base. So any triangle has three bases.
A trapezoid is a quadrilateral with at least one pair of parallel sides (indicated below in red). These parallel sides in a trapezoid are called bases.
Triangle ABC, quadrilateral DEFG, and pentagon HIJKL are each inscribed in a circle. Notice for each inscribed polygon, all the vertices lie on the circle and the polygon lies entirely inside the circle. The circles that surround the polygons are called circumcircles.
Enter your answer in the left column, then press tab
Angles and Triangles in a Circle: Investigate properties of inscribed triangles.
N-Sided Circle?: Compare the perimeters of polygons to the circumference of a circle. Inscribed Parallelogram: What can you tell about a parallelogram that is inscribed in a circle? Half is much may be right: Explore triangles inscribed in semicircles. Triangles inscribed inside triangles: Explore properties of triangles constructed using the midpoint of given triangles. Pentagram Triangles: How many triangles are formed?
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