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10.2: Inscribed Angle Theorem

Difficulty Level: At Grade Created by: CK-12

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

Problem 1 – Inscribed Angle Theorem

Start the Cabri Jr. application by pressing the APPS key and selecting Cabri Jr. Open the file INSCRIB1 by pressing Y=, selecting Open..., and selecting the file. In INSCRIB1, you are given circle D with radius AD. Angle ADB is a central angle and ACB is an inscribed angle.

1. Move point A to 2 different positions and point C to 2 different positions and collect the data in the table below. Calculate the ratios of mACB to mADB for each position and record the calculation in the table below.

Position Measure of ACB Measure of ADB mACBmADB
1
2
3
4

2. Angles ACB and ADB are said to intercept the same arc, AB, because they go through the same points A and B on the circle. An inscribed angle in a circle is __________ the measure of the central angle that intercepts the same arc on the circle.

Open the file INSCRIB2. You are given circle D. Angles ACB and AEB are inscribed angles and intercept the same arc.

3. Move point A to 2 different positions and move point E to 2 different positions and collect the data in the table below.

Position Measure of ACB Measure of AEB
1
2
3
4

4. Make a conjecture about two inscribed angles who intercept the same arc in a circle.

Open the file INSCRIB3. You are given circle D. Use this file to answer the following questions.

5. In circle D, what kind of segment is AB?

6. In circle D, what is mACB? (Hint: Use your answer to Exercise 4 to help you.).

Problem 2 – Extension of the Inscribed Angle Theorem

Open the file INSCRIB4. You are given circle D, AB, and ACB. Point G is a point on AB, ACB is an inscribed angle, and AG and BG are lines.

7. Move point A to 2 different positions and move point G to 2 different positions and collect the data in the table below.

Position Measure of ACB Measure of ADB Measure of AGE
1
2
3
4

8. Make a conjecture: The angle formed by the intersection of AG and BG is _______ the measure of the central angle ADB.

Open the file INSCRIB5. You are given circle D, arc AB, and ACB. Point G is a point on arc AB and ACB is an inscribed angle. Also, you are given chord AB and a tangent line BE.

9. Move point A to 2 different positions and move point B to 2 different positions and collect the data in the table below.

Position Measure of ACB Measure of ADB Measure of ABE
1
2
3
4

10. Make a conjecture: The angle between a chord and the tangent line at one of its intersection points equals ______________ of the central angle intercepted by the chord.

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TI.MAT.ENG.SE.1.Geometry.10.2

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