Education Technology

# Activities

• ##### Subject Area

• Maths: Geometry: Circles

9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Software

Cabri Geometry™
TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 18 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

## Relationship of Angles to the Circle

#### 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.

• 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