Relationship of Angles to the Circle

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Geometry: Circles

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-84 series

Applications

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Other Materials

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

Resource Types

Lessons

Report an Issue

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.

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

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix A PDF Teacher Notes Appendix B PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Geometry: Circles

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-84 series

Applications

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Other Materials

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

Resource Types

Lessons

Report an Issue

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Relationship of Angles to the Circle

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Relationship of Angles to the Circle

Before the Activity Files

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

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