In this investigation, you will explore the relationships in the sides of a triangle as well as compare the measures of the angles to the sides opposite to learn about the Triangle Inequality Theorems.

[color=#1551b5][b]Use the triangles above to answer the following questions.[/b][br][br]1. Move the points so that [math]angle[/math] A is the largest angle of Triangle ABC. Which side has the longest side length?[br][br]2. Move the points so that [math]angle[/math] A is the smallest angle of Triangle ABC. Which side has the shortest side length?[br][br]3. What conjecture can you make?[br][br][br]4. If m<A is greater than m<B and m<B is greater than m<C, write an inequality for the side measures.[br][br][br]5. Move the points to make side DE the longest side of Triangle DEF. Which angle is the largest?[br][br]6. Move the points to make side DE the shortest side of Triangle DEF. Which angle is the smallest?[br][br]7. What conjecture can you make?[br][br][br]8. If DE is greater than EF and EF is greater than FD, write an inequality for the angle measures.[br][br]9. Explore Triangle Inequalities in one Triangle more by clicking on the link below. After your investigation, complete the practice problems.[br][br][url]http://www.mathsisfun.com/geometry/triangle-inequality-theorem.html[/url][/color]