Download Sample 5.3.B.2 Complete

G.C.1-4
2011
Domain Circles
Cluster Understand and apply theorems about circles
Standards
1. Prove that all circles are similar.
2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed,
and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where
the radius intersects the circle.
3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a
circle.
4. (+) Construct a tangent line from a point outside a given circle to the circle.
Essential Questions
Enduring Understandings
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Why are all circles
similar?
How can you prove
relationships between
angles in a circle?
When lines intersect a
circle, or within a
circle, how do you find
the measures of
resulting angles?
What is the relationship
between inscribed and
circumscribed figures?
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Students will understand the
different components of
circles and how they relate to
angle measurements.
Students will understand that
inscribed angles on a diameter
are right angles.
Students will understand that
the radius of a circle is
perpendicular to the tangent
where the radius intersects the
circle.
Activities, Investigation, and Student Experiences
1. Interactive examples, PowerPoint lessons, regular level
and challenge level problems, sketchpad activities, and
hands on activities
2. Video and Interactive Examples
3. Sample Lessons and Examples
4. SMARTboard Slides with examples
G.C.1-4
Content Statements
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Students will be able to
use the fact that the
ratio of diameter to
circumference is the
same for circles to
prove that all circles are
similar.
Students will be able to
use definitions,
properties, and
theorems, to identify
and describe relations
among inscribed angles,
radii, and chords
(including central,
inscribed, and
circumscribed angles.)
Students will be able to
construct inscribed
circles of a triangle.
Students will be able to
construct circumscribed
circles of a triangle.
Students will be able to
use definitions,
properties, and
theorems to prove
properties of angles for
a quadrilateral inscribed
in a circle.
Students will be able to
2011
G.C.1-4
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find the measure of an
inscribed angle.
Students will be able to
find the measure of an
angle formed by a
tangent and a chord.
Students will be able to
construct a tangent line
from a point outside a
given circle to the
circle.
Assessments
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Student Participation
Questioning
Quizzes (Teacher Given and Self Quizzes):
o http://teachers.henrico.k12.va.us/math/igo/
08Circles/8-1Terminology/8-1t.htm
o http://teachers.henrico.k12.va.us/math/igo/
08Circles/8-3Tangents/8-3t.htm
o http://teachers.henrico.k12.va.us/math/igo/
08Circles/8-4ArcsChords/8-4t.htm
o http://teachers.henrico.k12.va.us/math/igo/
08Circles/8-5AngleFormulas/8-5t.htm
o http://teachers.henrico.k12.va.us/math/igo/
08Circles/8-6SegmentFormulas/8-6t.htm
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Benchmark/Test (Click here for resource folder)
http://sites.google.com/site/ppshighschoolmath/ho
me/benchmark-assessments/assessment
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Homework
2011
G.C.1-4
Equipment Needed:
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SMARTboard
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Projector
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Paper and pencil
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Calculator
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Compass
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Ruler
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Protractor
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Geometer’s Sketchpad
2011
Teacher Resources:
1. Henrico County Public Schools:
http://teachers.henrico.k12.va.us/math/igo/08Circles/8_1.htm
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http://teachers.henrico.k12.va.us/math/igo/08Circles/8_3.htm
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http://teachers.henrico.k12.va.us/math/igo/08Circles/8_4.htm
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http://teachers.henrico.k12.va.us/math/igo/08Circles/8_5.htm
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http://teachers.henrico.k12.va.us/math/igo/08Circles/8_6.htm
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2. Math Warehouse:
http://www.mathwarehouse.com/geometry/circle/interactivecentral-angle-of-circle.php
http://www.mathwarehouse.com/geometry/circle/inscribedangle.html#inscribedAngleDemo
http://www.mathwarehouse.com/geometry/circle/tangent-tocircle.php
3. Click here for Resource Folder.
4. Click here for Resource Folder.