10.2: Inscribed Angle Theorem
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 CabriJr. Open the file INSCRIB1 by pressing , selecting Open..., and selecting the file. In INSCRIB1, you are given circle with radius . Angle is a central angle and is an inscribed angle.
1. Move point to 2 different positions and point to 2 different positions and collect the data in the table below. Calculate the ratios of to for each position and record the calculation in the table below.
Position | Measure of | Measure of | |
---|---|---|---|
1 | |||
2 | |||
3 | |||
4 |
2. Angles and are said to intercept the same arc, , because they go through the same points and 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 . Angles and are inscribed angles and intercept the same arc.
3. Move point to 2 different positions and move point to 2 different positions and collect the data in the table below.
Position | Measure of | Measure of |
---|---|---|
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 . Use this file to answer the following questions.
5. In circle , what kind of segment is ?
6. In circle , what is ? (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 , , and . Point is a point on , is an inscribed angle, and and are lines.
7. Move point to 2 different positions and move point to 2 different positions and collect the data in the table below.
Position | Measure of | Measure of | Measure of |
---|---|---|---|
1 | |||
2 | |||
3 | |||
4 |
8. Make a conjecture: The angle formed by the intersection of and is _______ the measure of the central angle .
Open the file INSCRIB5. You are given circle , arc , and . Point is a point on arc and is an inscribed angle. Also, you are given chord and a tangent line .
9. Move point to 2 different positions and move point to 2 different positions and collect the data in the table below.
Position | Measure of | Measure of | Measure of |
---|---|---|---|
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.