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