## Final V

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For this problem we were asked to pick one of the problems that we thought was our best work of the quarter. I choose to submit some of my script files (made in GSP) from assignment 5. The script files that I submitted are the ones that were very helpful to me for most of the quarter. Using these different script files, I performed numerous and various investigations on triangles. Please see the following script files:

1) Construction of the centroid (G) of a triangle
2) Construction of the orthocenter (H) of a triangle
3) Construction of the circumcenter (C) of a triangle
4) Construction of the incenter (I) of a triangle
5) Construction of G, H, C, and I of a triangle

I used these files to do numerous investigations on the centers of triangles and how these centers changed with different kinds of triangles. See write up four for some of these investigations.

### Construction of the centroid (G)

Construction of the centroid (G) of triangle ABC given the vertices of the triangle. The centroid is the intersection of the three medians of the triangle.

### Construction of the orthocenter (H)

Construction of the orthocenter (H) of triangle ABC given the vertices A, B, and C. The orthocenter of a triangle is the common intersection point of the three lines containing the altitudes.

### Construction of the circumcenter (C)

Construction of the circumcenter (C) of triangle ABC given the verticies A, B, and C. The circumcenter is the point in the plane equidistant from the three vertices of the triangle.

### Construction of the incenter (I)

Construction of the incenter (I) of triangle ABC given the verticies A, B, and C. The incenter is the point on the interior of the triangle that is equidistant from the three sides.