Explorations in Geometry

with the

Geometer’s Sketchpad

Exploration 4.

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- Construct a triangle ABC and one point on each side to form triangle DEF. Measure the perimeter of triangle DEF. Now adjust the three points D,E , and F until the perimeter is a minimum. What do you notice about the location of the points that yield the minimum perimeter?
- Construct the angle bisectors of triangle DEF, what do you notice about these lines when the perimeter is a minimum?
- Adjust the triangle ABC to different shapes to test your conjectures…. Is it true for right triangles, obtuse triangles???
- What other patterns and relations can you discover about this shape?

5) Write a brief paragraph and describe the relationships you have observed in this exploration.