Activity Overview
In this activity, students recognize the relationship of angles to its circles. They study the Inscribed Angle Theorem and its corollaries.
Before the Activity
Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:
TI-Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable
TI-Navigator™ "send to class" feature
See the attached PDF file for detailed instructions for this activity
Print pages 71 - 74 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Construct a circle
Draw two secants to create an inscribed angle (an angle formed by two secants whose point of intersection lies on the circle)
Measure the inscribed angle
Measure the arc opposite the inscribed angle (intercepted arc)
Observe that the measure of the inscribed angle is half the measure of the intercepted arc
Alter the angle and verify the relationship
Construct a circle
Draw two secants to create an interior angle (an angle formed by two secants that intersect inside the circle)
Measure the interior angle
Measure the arcs intercepted by the angle
Observe that the measure of the interior angle is half the sum of the measures of its intercepted arcs
Alter the angles and verify the observations
Construct a circle
Draw two secants to create an exterior angle (an angle formed by two secants that intersect outside the circle)
Measure the exterior angle
Measure the intercepted arcs
Observe that the measure of an exterior angle is half the difference of measures of its intercepted arcs
Alter the angles and verify the relationship
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary