Geometry Building Blocks: Polygons

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A series of free, online High School Geometry Video Lessons and solutions. Examples, solutions, videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

  • what are polygons
  • what are the types of triangles
  • how to find the perimeter
  • what are the parts of a circle


Polygons are closed plane figures formed by three or more line segments. If a figure is open or curved, it cannot be considered a polygon. Concave polygons have at least one diagonal that does not pass through the interior of the polygon; all of the diagonals in a convex polygon are contained within the figure. Equiangular polygons have all angles congruent; equilateral polygons have all sides congruent.
How to define a polygon, how to distinguish between concave and convex polygons, how to name polygons?

Types of Triangles

Triangles can be classified by their angle measures and side lengths. For triangles only, equiangular and equilateral have the same implications: all sides and angles are congruent. Isosceles triangles have at least two congruent sides and two congruent angles. Right triangles contain an angle whose measure is 90 degrees. All the angles in an acute triangle are less than 90 degrees. Knowing the different types of triangles is important when solving proofs.
This video shows the three main types of triangles and their features.
Classifying triangles by angles and sides.


Perimeter is the sum of the sides of a polygon. It is a distance and therefore is a one-dimensional property. The perimeter of a circle is called its circumference, and can be found using the formula Circumference = 2(pi)(radius). For a square, the perimeter = 4(side length), and for a rectangle, perimeter = 2(length of the width) + 2(length of the height).
Finding the perimeter of rectangles, triangles, and other polygons is covered in this video.

Parts of a Circle

A chord is a line segment whose endpoints are on a circle. A diameter is a chord that passes through the center of a circle. Another one of the parts of a circle is a radius, which is a line segment with one endpoint at the center and one endpoint on the circle. Congruent circles have congruent radii (the plural of radius). Concentric circles have the same center. A central angle has a vertex on the center and endpoints on the circle.
How to define a circle and identify its main parts?

This video explains the parts of a circle, including center point, radius, chord, diameter, central angle, arc, and sector. It also shows you what mathematical tool you use to draw circles.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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