Triangle inequalities
Task
Create an applet that illustrates the construction steps for a triangle whose three side lengths a , b and c are given. Additionally, this applet will allow you to discover triangle inequalities.
Note: The triangle inequalities a + b > c, b + c > a and a + c > b state that the sum of two side lengths of a triangle is greater than the length of the third side of the triangle. If the triangle inequalities are not fulfilled for a certain set of side lengths, it is not possible to construct a triangle using the given lengths.
Explore the construction...
Instructions
| 1. |  | Create sliders a, b and c for the side lengths of the triangle with an interval from 0 to 10 and Increment 0.5 each. |
| 2. |  | Set the slider values to a = 8, b = 6.5 and c = 10. |
| 3. |  | Create segment f with given length c. Hint: Points A and B are the endpoints of the segment. |
| 4. |  | Create a circle d with center A and radius b. |
| 5. | | Create a circle e with center B and radius a. |
| 6. |  | Construct the intersection point C of the two circles e and f. |
| 7. |  | Create the triangle ABC. |
| 8. |  | Create interior angles , and of triangle ABC. |
Try it yourself...
Instructions (continued)
| 9. |  | Create a point D on circle d. |
| 10. |  | Create segment g between the points A and D. |
| 11. |  | Construct the midpoint E of segment g. |
| 12. |  | Enter text1: b and attach it to point E.
Hint: After selecting the Text tool, click on point E. Open Advanced and select b from the  Objects tab.
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| 13. |
| Create a point F on circle e. |
| 14. | 
| Create segment h between the points B and F. |
| 15. |  | Construct the midpoint G of segment h. |
| 16. | 
| Enter text2: a and attach it to point G. |
| 17. | 
| Hide points D, E, F and G by using the Show / Hide Object tool. |
| 18. |  | Enhance your construction by using the Style Bar and match colors of corresponding objects. |