Explorations in Geometry
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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.