<meta http-equiv="refresh" content="1; url=/nojavascript/"> Inscribed Angles Theorem | CK-12 Foundation
Dismiss
Skip Navigation
You are reading an older version of this FlexBook® textbook: CK-12 Texas Instruments Geometry Teacher's Edition Go to the latest version.

10.2: Inscribed Angles Theorem

Created by: CK-12

This activity is intended to supplement Geometry, Chapter 9, Lesson 4.

ID: 12437

Time Required: 15 minutes

Activity Overview

Students will begin this activity by looking at inscribed angles and central angles and work towards discovering a relationship among the two, the Inscribed Angle Theorem. Then, students will look at two corollaries to the theorem.

Topic: Circles

  • Construct central and inscribed angles
  • Inscribed angles theorem

Teacher Preparation and Notes

Associated Materials

  • Student Worksheet: Inscribed Angle Theorem http://www.ck12.org/flexr/chapter/9694, scroll down to the second activity.
  • Cabri Jr. Application
  • INSCRIB1.8xv, INSCRIB2.8xv, INSCRIB3.8xv, INSCRIB4.8xv, and INSCRIB5.8xv

Problem 1 – Similar Triangles

Students will begin this activity by looking at inscribed angles and central angles and work towards discovering a relationship among the two.

Students will be asked to collect data by moving points A and C. Students are asked questions about the relationships in the circle and are asked to make a conjecture. In order to calculate the ratio of m\angle{ACB} to m\angle{ADB}, students can use the Calculate tool in the Actions menu.

On page 1.6, students will look at two inscribed angles intercepted by the same arc and are asked to make a conjecture about the relationship.

In an advanced setting a proof of the inscribed angle theorem and the two conjectures in problem one are appropriate and can be proved using isosceles triangles.

Problem 2 – Extension of the Inscribed Angle Theorem

In Problem 2, students will look at two more angles created from the central angle and the intercepted arc. Both sections of this problem are corollaries of the Inscribed Angle Theorem and both solutions are congruent to the measure of the central angle intercepted by the arc or one-half the measure of the central angle.

Solutions

1. Sample answers

Position Measure of \angle{ACB} Measure of \angle{ADB} \frac{m\angle{ACB}}{m\angle{ADB}}
1 36.65^\circ 73.30^\circ 0.5
2 49.50^\circ 99.01^\circ 0.5
3 49.50^\circ 99.01^\circ 0.5
4 49.50^\circ 99.01^\circ 0.5

2. \frac{1}{2}

3. Sample answers

Position Measure of \angle{ACB} Measure of \angle{AEB}
1 36.65^\circ 36.65^\circ
2 48.30^\circ 48.30^\circ
3 48.30^\circ 48.30^\circ
4 48.30^\circ 48.30^\circ

4. Sample answer: They are congruent.

5. diameter of the circle

6. 90^\circ

7. Sample answers

Position Measure of \angle{ACB} Measure of \angle{ADB} Measure of \angle{AGE}
1 36.65^\circ 73.30^\circ 36.65^\circ
2 67.04^\circ 134.10^\circ 67.04^\circ
3 67.04^\circ 134.10^\circ 67.04^\circ
4 67.04^\circ 134.10^\circ 67.04^\circ

8. \frac{1}{2}

9. Sample answers

Position Measure of \angle{ACB} Measure of \angle{ADB} Measure of \angle{ABE}
1 57.65^\circ 115.30^\circ 57.64^\circ
2 49.20^\circ 98.40^\circ 49.19^\circ
3 54.90^\circ 109.80^\circ 54.90^\circ
4 63.55^\circ 127.10^\circ 63.54^\circ

10. \frac{1}{2}

Image Attributions

Description

Categories:

Grades:

Date Created:

Feb 23, 2012

Last Modified:

Aug 19, 2014
Files can only be attached to the latest version of None

Reviews

Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
TI.MAT.ENG.TE.1.Geometry.10.2

Original text