This lesson is to be used to discover relationships between central angles, inscribed angles and the measure of the intercepted arc.[br]Follow the directions and answer the questions below.
[b]Directions:[/b][br]o Check on the checkbox to Show[color=#ff0000] Central Angle[/color] and its [color=#ff0000]Measure[/color][br]o Check on the checkbox to Show[color=#0000ff] Arc[/color] and its [color=#0000ff]Measure[/color][br]o Drag points C and D and record at least three measures:[br][list=1][*]< 180[sup]o[/sup][/*][*][sup] [/sup]= 180[sup]o[/sup][/*][*]> 180[sup]o[/sup][br][sup][/sup][/*][/list][br][b][color=#0000ff]Make a conjecture about the relationship between a central angle and its intercepted arc:[/color][/b]
The measure of the [color=#ff0000]Central Angle[/color] equals the measure of its [color=#0000ff]Arc[/color].
[b]Directions:[/b][br]o Check on the checkbox to Show Inscribed Angle and its Measure[br]o Drag points E, C and D and record at least three measures:[br][list=1][*]< 180[sup]o[/sup][/*][*][sup] [/sup]= 180[sup]o[/sup][/*][*]> 180[sup]o[/sup][br][sup][/sup][/*][/list][br][b][color=#0000ff]a) Make a conjecture about the relationship between a central angle and an inscribed angle.[br][br]b) Make a conjecture about the relationship between an inscribed angle and its interecepted arc.[/color][/b]
a) The measure of the Inscribed Angle equals one-half of the measure of its [color=#0000ff][color=#ff0000]Central Angle[/color][/color].[br][br]b) The measure of the Inscribed Angle equals one-half of the of its Intercepted Arc.