Central Angles, Arc Measure and Length, and Arc Addition Postulate.

Could you determine the differences, and similarities between angular measure of one arc, and its length? Do you know the difference among a minor arc, a semicircle, and a major arc? Do you know the relationship between an arc, and its central angle? Do you know how to use Arc Addition Postulate?

This lesson will teach you in very easy to follow terms, how to answer to all these questions. You will have the opportunity to explore each one of the concepts behind most of them. In this highly visually rich environment you won't be slowed down by long narratives. This is the breakthrough lesson you were waiting for!

Lesson's Content

Lesson's Glossary

Arc
Curved segment in a circle.

Arc length
The distance between an arc's endpoints along the path of the circle.

Center of a circle
The point that all points in the circle are equidistant from.

Central angle of a circle
An angle whose vertex is the center of the circle. 

Circle
The set of points on a plane at a certain distance (radius) from a certain point (center); a polygon with infinite sides.

Circumference
The perimeter of a circle.

Clockwise
An orientation, the direction in which the points are named when, if traveling along the line, the interior of the polygon is on the right.

Compass
A drawing tool used to draw circles at different radii.

Counterclockwise
In orientation, the direction in which points are named when, if travelling on the line, the interior of the figure is on the left side.

Minor arc
An arc whose endpoints form an angle less than 180 degrees with the center of the circle.

Major arc
An arc whose endpoints form an angle over 180 degrees with the center of the circle.

Pi
Greek letter used in geometry to represent the ratio of the circumference to the diameter and whose value is approx. 3.1416 (irrational number)

Radii
Plural form of radius.

Radius
The segment whose endpoints are any point on a circle or sphere and its center; the length of that segment.

Sector
Part of a circle containing its center and an arc.

Semicircle
An arc whose central angle is a right angle.

Interactive Geometric Applets: Relevant Theorems.

An arc has the same angular measure as its central angle, and an inscribed angle intersecting

the same arc is half the angular measure of that central angle.

This interactive applet allows you to drag point "A" or point "B" and verify this relationship.

You may also check how the arc length is updated in the equation at the upper right corner of

the applet.

Vocabulary Puzzle Interactive

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