UGA logo

Assignment 4

by

Allison McNeece


 

Medial triangle:

Constructing any triangle and then find the mid points of the sides. Connect these points to form a smaller triangle inside the original triangle. This smaller triangle is the medial triangle.

Here is one for you to play with. Click and drag any vertice to explore how the medial triangle changes:

 

Sorry, this page requires a Java-compatible web browser.

medial triangle


 

Orthic Triangle:

Construct any acute triangle. From each angle, construct a line that is perpindicular to the opposite side. The points where these lines intersect the sides are the vertices of the orthic triangle.

 

Sorry, this page requires a Java-compatible web browser.

When does the orthic triangle disappear?

 


 

Orthocenter-Midsegment Triangle:

Construct any triangle and find the orthocenter. Then construct segments from the orthocenter to each vertex. Find the midpoints of these segments and connect them to form the orthocenter-midsegment triangle.

Sorry, this page requires a Java-compatible web browser.

When is orthocenter-midsegment triangle outside of the larger triangle?

 


 

All together now:

Now let's put it all together and observe each triangles circumcenter:

Sorry, this page requires a Java-compatible web browser.

hmmmm.... they all have the same circumcenter

 

Since they all have the same circumcenter it follows that they all have the same circumcircle

 

Sorry, this page requires a Java-compatible web browser.

This is the 9-point circle.


This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.

 


return to my page