Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Circles

9-12

90 Minutes

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

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 27 from the EXPLORATIONS Book:
Cabri™ Jr.: Interactive Geometry Activities and Investigations.

## Angles Formed by Intersecting Chords, Secants, and Tangents

#### 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