Description: MM2G3. Students will understand the properties of circles. Elements: a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
b. Understand and use properties of central, inscribed, and related angles.
c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.
d. Justify measurements and relationships in circles using geometric and algebraic properties.
A central angle is an angle whose vertx is the center of a circle, and whose sides pass through a pair of points on the circle, thereby subtending an arc between those two points whose angle is equal to the central angle itself.
Summary:
Theorem 68:
In a circle, if two central angles have equal measures,
then their corresponing minor arcs have equal measures.
Example:
A circle is divided into 4 congruent sectors and each of them is divided into 3 congruent sectors as in the figure.
What is the measure of the central angle POQ in degrees?
A. 45
B. 30
C. 90
D. 60
Correct Answer: D Solution: Step 1: Central angle of each sector = (360/12)° = 30° Step 2: Measure of the central angle POQ is 2(30) = 60.
Elements:
a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
b. Understand and use properties of central, inscribed, and related angles.
c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.
d. Justify measurements and relationships in circles using geometric and algebraic properties.
A central angle is an angle whose vertx is the center of a circle, and whose sides pass through a pair of points on the circle, thereby subtending an arc between those two points whose angle is equal to the central angle itself.
Summary:
Theorem 68:
In a circle, if two central angles have equal measures,
then their corresponing minor arcs have equal measures.
Example:
A circle is divided into 4 congruent sectors and each of them is divided into 3 congruent sectors as in the figure.
What is the measure of the central angle POQ in degrees?
A. 45
B. 30
C. 90
D. 60
Correct Answer: D
Solution:
Step 1: Central angle of each sector = (360/12)° = 30°
Step 2: Measure of the central angle POQ is 2(30) = 60.
"Geometry: Central Angles and Arcs - CliffsNotes." Pass Your Tests and Homework with CliffsNotes Study Guides - CliffsNotes. Web. 16 Dec. 2009. http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Central-Angles-and-Arcs.topicArticleId-18851,articleId-18824.html.
"Central angle -." Wikipedia, the free encyclopedia. Web. 16 Dec. 2009. http://en.wikipedia.org/wiki/Central_angle.
Web. 16 Dec. 2009. <http://www.icoachmath.com/SiteMap/CentralAngle.html>.