[color=#000000]Interact with this applet for a few minutes, then answer the questions that follow. Be sure to change the locations of the triangle's [/color][color=#ff00ff][b]PINK VERTICES[/b][/color][color=#000000] before and after sliding the slider! [/color]

[color=#000000][b]Questions:[/b] [br][br]1) What can you conclude about the 3 white points? How do you know this? [br]2) What is the measure of each [/color][b]gray angle[/b][color=#000000]? How do you know this? [br]3) What vocabulary terms best describes each [/color][color=#980000][b]brown dotted line[/b][/color][color=#000000]? Why is this? [br]4) Describe [/color][color=#1e84cc][b]the intersection[/b][/color][color=#000000] of these [/color][color=#980000][b]3 brown dotted lines[/b][/color][color=#000000]. [/color][color=#1e84cc][b]How do they intersect?[/b][/color][color=#000000] [br][br]5) Use the angle tool to now measure and display the measures of this triangle's [/color][color=#38761d]3 interior angles[/color][color=#000000]. [br][/color][color=#000000] For [/color][color=#38761d]angle measures > 180 degrees[/color][color=#000000], use the menu (upper right hand corner) to adjust this.[br][br][/color][color=#1e84cc][b]Point C[/b][/color][color=#000000] is called the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] of the triangle. [br]Drag the [/color][color=#ff00ff][b]pink vertices[/b][/color][color=#000000] around to help you answer the new few questions. [br][br]6) Is it ever possible for the [/color][color=#1e84cc][b]circumcenter [/b][/color][color=#000000]to lie [i]outside the triangle[/i]?[br] If so, how would you classify such a triangle by its angles? [br][br]7) Is it ever possible for the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] to lie [i]on the triangle itself[/i]?[br] If so, how would you classify such a triangle by its angles? [br] And if so, where exactly on the triangle is the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] found? [br][br]8) Is it ever possible for the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] to lie [i]inside the triangle[/i]?[br] If so, how would you classify such a triangle by its angles? [br][br]9) What is so special about the [/color][color=#38761d][b]green circle[/b][/color][color=#000000] with respect to the triangle's [/color][color=#ff00ff][b]pink vertices[/b][/color][color=#000000]? [br][br]10) What [/color][color=#ff0000]previously learned theorem[/color][color=#000000] easily implies that the distance from the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] to any [/color][color=#ff00ff][b]vertex[/b][/color][color=#000000] [br] is equal to the distance from the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] to any other [/color][color=#ff00ff][b]vertex[/b][/color][color=#000000]? [/color]

[color=#000000][b]Questions:[/b] [br][br]1) What can you conclude about the 3 white points? How do you know this? [br][br][br]2) What is the measure of each [/color][b]gray angle[/b][color=#000000]? How do you know this? [br][br][br]3) What vocabulary terms best describes each [/color][color=#980000][b]brown dotted line[/b][/color][color=#000000]? Why is this? [br][br][br]4) Describe [/color][color=#1e84cc][b]the intersection[/b][/color][color=#000000] of these [/color][color=#980000][b]3 brown dotted lines[/b][/color][color=#000000]. [/color][color=#1e84cc][b]How do they intersect?[/b][/color][color=#000000] [br][br][br][br]5) Use the angle tool to now measure and display the measures of this triangle's [/color][color=#38761d]3 interior angles[/color][color=#000000]. [br][/color][color=#000000] For [/color][color=#38761d]angle measures > 180 degrees[/color][color=#000000], use the menu (upper right hand corner) to adjust this.[br][br][br][br][/color][color=#1e84cc][b]Point C[/b][/color][color=#000000] is called the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] of the triangle. [br]Drag the [/color][color=#ff00ff][b]pink vertices[/b][/color][color=#000000] around to help you answer the new few questions. [br][br]6) Is it ever possible for the [/color][color=#1e84cc][b]circumcenter [/b][/color][color=#000000]to lie [i]outside the triangle[/i]?[br] If so, how would you classify such a triangle by its angles? [br][br]7) Is it ever possible for the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] to lie [i]on the triangle itself[/i]?[br] If so, how would you classify such a triangle by its angles? [br] And if so, where exactly on the triangle is the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] found? [br][br]8) Is it ever possible for the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] to lie [i]inside the triangle[/i]?[br] If so, how would you classify such a triangle by its angles? [br][br]9) What is so special about the [/color][color=#38761d][b]green circle[/b][/color][color=#000000] with respect to the triangle's [/color][color=#ff00ff][b]pink vertices[/b][/color][color=#000000]? [br][br]10) What [/color][color=#ff0000]previously learned theorem[/color][color=#000000] easily implies that the distance from the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] to any [/color][color=#ff00ff][b]vertex[/b][/color][color=#000000] [br] is equal to the distance from the [/color][color=#1e84cc][b]circumcenter[/b][/color][color=#000000] to any other [/color][color=#ff00ff][b]vertex[/b][/color][color=#000000]? [/color]