Triangle inequality

Drag the vertices of ABE to form acute, obtuse, and right triangles. Make conjectures about each type of triangle.
Construct a few obtuse, acute, and right triangles by dragging vertices A, B, E. Make conjectures about the segment lengths of each type of triangle AS A WHOLE. In other words, compare sums, differences, and even squares of side lengths. Sides are labelled a, b, c, so you should be thinking about some "random" formula which uses a, b, c (hint, hint, *cough*, nudge, nudge). ALSO, make conjectures about the areas of the squares built on each segment. Finally, compare the angles of the triangle to the segments opposite them. Is there a relationship between the location of the smallest segment or angle and largest segment or angle? Collect data. See what inferences you can make.