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Chapter 6--Discovering and Proving Circle Properties

Essential Question:  How can the properties of circles be used to identify and prove theorems?

Unit Rationale:  Extending the properties and theorems of triangles to convex polygons to circles further widens our repertoire of two-dimensional physical shapes and prepare us for future applications of three-dimensional shapes, such as cylinders and spheres.

As a result of this unit, students will be able to:

Ø  Identify the basic structure of a circle.

Ø  Identify, prove, and apply the properties of circles:

§  Angle conjectures (Central, Inscribed, Interior, Exterior, Tangent-Secant, and tangent-Tangent)

§  Angles inscribed in a semicircle

§  Relationships between circumference, diameter, radius, and pi.


·        Circle/center/radius/diameter

·        Central angle/Inscribed angle Space

·        Tangent line

·        Arc/Intercepted arc

·        Arc length

·        Pi

·        Circumference

Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements. 

Focus Standards:

G.3.H  Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles.

G.3.I  Explain and perform constructions related to the circle.

G.6.A  Derive and apply formulas for arc length and area of a sector of a circle.

Supporting Standards:

*G.6.E  Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.

Reasoning, Problem Solving, and Communication Standards:

G.7.D  Generalize a solution strategy for a single problem to a class of related problems and apply a strategy for a class of related problems to solve specific problems.

G.7.H  Use inductive reasoning to make conjectures , and use deductive reasoning to prove or disprove conjectures.