Centers of a triangle

1. Use Geometer's Sketchpad (GSP) to Construct the centroid and explore its location for various shapes of triangles.

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2. Use GSP to construct an orthocenter H and explore its location for various shapes of triangles. (Make sure your construction holds for obtuse triangles.)

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3. Construct the circumcenter C and explore its location for various shapes of triangles. It is the center of the CIRCUMCIRCLE (the circumscribed circle) of the triangle.

The centroid of a triangle is the common intersection of three medians. A median of a triangle is the segment from a vertex to the midpoint of the opposite side. Here, D,E,F are the midpoint of each segment BC, AC, and AB. G is the point of intersection of AD, BE, and CF and it is called the centroid of a triagle ABC.

The centroid is two-thirds the distance from each vertex to the opposite side. For example, BG=(2/3)(BE).

By dragging one of the vertex, triangle ABC is moving with different values of BG and BE. However, the rate of the BG/BE is a constant.