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ADDITIONAL INFORMATION FOR TEACHER

 Brainstorm with students the possible different points that could be constructed. Below is a list of some of those points.

1. Construct the line segments AB and BC, then compute their sum.
2. Construct the line segments AB and AC, then compute their sum.
3. Construct the line segments BC and AC, then compute their sum.
4. Construct the centroid (D) of the triangle formed by the points A, B, and C , then measure the distances AD, BD, and CD, and finally compute the sum of these three distances.
5. Construct the orthocenter (O) of the triangle formed by the points A, B, and C , then measure the distances AO, BO, and CO, and finally compute the sum of these three distances.
6. Construct the incenter (I) of the triangle formed by the points A, B, and C , then measure the distances AI, BI, and CI, and finally compute the sum of these three distances.
7. Construct the circumcenter (T) of the triangle formed by the points A, B, and C , then measure the distances AT, BT, and CT, and finally compute the sum of these three distances.
8. Construct point M such that the measure of angles MAB and MBA is 30º.
9. Construct point N such that the measure of angles NAB and NBA is 45º.
10. Construct one other point (P) of your choosing and measure the distances PA, PB, and PC. Then find the sum of these three distances.

Allow students to use The Geometer's Sketchpad and analytic geometry if they request.

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