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.
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.