# Geometry: Circles and Polygons 185

This class explains basic circle and polygon geometry and how their features are used to find dimensions in sample shop drawings.

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## Class Details

Class Name:
Geometry: Circles and Polygons 185
Description:
This class explains basic circle and polygon geometry and how their features are used to find dimensions in sample shop drawings.
Version:
1.0
Difficulty:
Beginner
Number of Lessons:
16
Spanish, Chinese
Related 2.0 Class:
Geometry: Circles and Polygons 171

## Class Outline

• Objectives
• What Is a Circle?
• Radius and Diameter
• Circumference
• Area of a Circle
• Angles and Circles
• Angles and Circles: Sample Problem
• Angles and Circles: Solution
• Tangents
• Tangents: Sample Problem
• Sample Tangent Problem: Solution
• What Is a Polygon?
• Types of Polygons
• Interior Angles
• Polygons: A Sample Problem
• Summary

## Objectives

• Define circle.
• Define diameter.
• Calculate the circumference of a circle using the value of pi.
• Calculate the area of a circle using the value of pi.
• Describe the relationship of all central angles within a circle.
• Distinguish between essential and nonessential information for solving a problem using circle geometry.
• Solve for missing angles in a sample bolt hole pattern.
• Define tangent.
• Distinguish between essential and nonessential information for solving a problem using a tangent.
• Solve for a missing angle in a sample tangent problem.
• Define polygon.
• List types of polygons.
• Calculate the sum of the interior angles for a sample polygon.
• Solve for a missing interior angle in a sample polygon problem.

## Certifications

SME
• CMfgT
NIMS
• Metalforming I
MSSC
• MSSC Quality Practices and Measurement

## Glossary

Vocabulary Term Definition
angle The distance between two rays sharing a common endpoint or two lines that intersect. An angle has one vertex and two sides.
angles of a circle The angles formed within a circle. All angles in a circle add up to 360 degrees.
area The size of the space contained within an enclosed two-dimensional figure. Area is typically measured in square units such as square inches or square centimeters.
bolt hole pattern A pattern used on some workpieces in which a series of holes are formed around an imaginary center.
central angle An angle formed within a circle in which the center of the circle is the vertex and the sides of the angle are radii.
circle The figure formed by the group of points that are an equal distance from a point, or center. The angles of a circle add up to 360 degrees.
circumference The boundary or perimeter around a circle. Circumference measures the distance around a circle.
concave polygon A polygon in which at least one of the angles is greater than 180 degrees.
convex polygon A polygon in which all angles are less than 180 degrees.
diameter The distance from one edge of the circle to the opposite end through the center. The radius is half the diameter.
hexagon A polygon with six sides.
perpendicular Two lines that intersect to form a 90° angle.
pi A special constant value that relates the diameter of a circle to its circumference. Pi, roughly 3.14, is used to find the circumference and area of a circle.
point of tangency The point at which the tangent touches the circle.
polygon A closed shape consisting of line segments that has at least three sides. Triangles, quadrilaterals, rectangles, and squares are all types of polygons.
quadrilateral A polygon with four sides.
radii The plural for radius. All radii on a given circle are equal in length.
radius The distance from the center to the edge of a circle. If you multiply the radius of a circle by two, the result is the diameter.
ratio The relationship between two quantities expressed as a fraction.
regular polygon A polygon in which all angles and sides are equal.
semicircle A half-circle. The angles of a semicircle add up to 180 degrees.
square The product of multiplying a number by itself.
tangent A line, line segment, or ray that touches a circle at exactly one point.
tangent point Another way to describe the point of tangency.
triangle A polygon with three sides.
vertex The point of an angle where its two sides meet.
vertical angle Two angles that share the same vertex and are positioned directly opposite one another. Vertical angles are formed whenever two lines intersect.
vertical angles Two angles that share the same vertex and are positioned directly opposite one another. Vertical angles are formed whenever two lines intersect.