Activity Overview
In this activity, students will investigate properties of angles and arcs formed when chords, secants, and tangents intersect and intercept arcs in a circle. They discover several important theorems concerning circles and arc sizes. They make use of the Central Angle theorem, which ensures that the measure of a central angle of a circle is equal to the measure of its intercepted arc.
Before the Activity
Install the Cabri Jr. App on the students' graphing calculators using TI Connect™, a TI Connectivity Cable and the Unit-to-Unit Link Cable
Use the TI-Navigator™ to transfer the attached Cabri Jr. AppVar files to each calculator
See the attached PDF file for detailed instructions for this activity
Print pages 179 - 183 from the attached PDF file for your class
During the Activity
Distribute the pages to your class.
Follow the Activity procedures:
Use the AppVar to go directly to the exploration section
Construct an angle inscribed in a circle and its corresponding central angle
Drag the points and observe changes in the angles
Construct a circle with two intersecting chords
Construct a circle with two secants that intersects outside the circle
Construct a circle which has a tangent and a chord that intersect at a point
Use the Calculate tool to investigate the relationship between the angles formed by the chords
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary