Points of Concurrency
Table of Contents
- Prerequisites
- Triangle Median Illustrator & Definition Writing Prompt
- Angle Bisector Definition (I)
- Triangle Altitude Illustrator & Definition Writing Prompt
- Perpendicular Bisector Definition
- Points of Concurrency
- Circumcenter & Circumcircle (A)
- Circumcenter Exploration (B)
- Incenter & Incircle (A)
- Incenter Exploration (B)
- Medians & Centroid (A)
- Medians Centroid Theorem (Proof without Words)
- Orthocenter (A)
Triangle Median Illustrator & Definition Writing Prompt
Interact with the applet for a few minutes. [br][br]The [b][color=#38761d]green segment[/color][/b] that will appear is said to be a [b]MEDIAN [/b]of the triangle. [br]Be sure to move the [b][color=#9900ff]purple vertex[/color][/b] of the triangle around a bit as well. [br][br]Answer the questions that appear below the applet and (alternate tutorial) video.
Alternate Tutorial
1.
Is it ever possible for a triangle's [color=#38761d][b]median[/b][/color] to lie outside the triangle?
2.
Use what you've observed to complete the following sentence definition (without looking it up on another tab in your browser): [br][br][i]A [b][color=#38761d]median [/color][/b]of a triangle is...[/i]
Circumcenter & Circumcircle (A)
[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]
1) What can you conclude about the 3 white points? How do you know this?
[color=#000000]2) What is the measure of each [/color][b]gray angle[/b][color=#000000]? How do you know this?[/color]
[color=#000000]3) What vocabulary terms best describes each [/color][color=#980000][b]brown dotted line[/b][/color][color=#000000]? Why is this?[/color]
[color=#000000]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]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.[/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.[/color]
[color=#000000]6) 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]?[/color]