Properties of Angles in Circles
Properties of Angles in Circles
Table of Contents
- Central and Inscribed Angles
- Central Angles, Inscribed Angles, and Intercepted Arcs
- Inscribed Quadrilaterals
- Circle With Inscribed Quadrilateral Investigation
Central Angles, Inscribed Angles, and Intercepted Arcs
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.
Central Angle and Arc Measure
[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]
Inscribed Angles and Arc Measures
[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][/*][/list][b][color=#0000ff][br]Make a conjecture about the relationship between an inscribed angle and its intercepted arc.[br][/color][/b]
Central Angles Vs. Inscribed Angles
[b][color=#0000ff][b][color=#0000ff]Make a conjecture about the relationship between a central angle and an inscribed angle.[/color][/b][/color][/b]
Circle With Inscribed Quadrilateral Investigation
Compare the angles by investigating the sums of angles.
What relationship do the angles of a quadrilateral inscribed in a circle have with each other?