Jessica Furr

Jessica (Furr) Waggener
University of Georgia
Department of Mathematics Education

EMT 468
October 16, 1996
Constructing a Technology-Rich Lesson

Inscribed Angles

I. Objectives

To recall the connection that arc measure refers to part of a circle and angle measure is based on central angles as intercepting part of circle.
To extend the connection to show that inscribed angles measure 1/2 of the intercepted arc.

II. Materials:

III. Class Directed To

IV. Assumed Previous Knowledge:

Definitions: circle, chords, vertexsquare, angle, angle types, arc measure, congruence, intercept

Familiarity with GSP and past experience in attempting to draw square.

V. Mathematical Activities:

see angles.gsp

Explore relationship between measure of angles and measure of arc. Generate measurement theorem with ratio.

Generate a definition of inscribed angles through comparison with "nots"; must include mention of vertex on circle and sides as chords.

Review connection with angle measure (central) and arc measure. Prove theorem with diameter. (also corollary)

Demonstrate congruent inscribed angles and generate 2nd corollary: Opposite angles of quadrilateral supplementary.

VI. Assignments:

Book exercises. Construct an inscribed SQUARE in GSP and DEFEND.

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