Triangle Constructions

Using GeoGebra like a DGS we constructed a triangle for given sides a, b and c with the tools "Segment with given length" and "Circle with center and radius". Click the forward button in the navigation bar to go through the construction step by step. Use the sliders to investigate whether this Side-Side-Side (SSS) construction is possible for any given lengths a, b and c.

Here is the construction protocol of a triangle for three given side lenghts (SSS):

• Draw segment AB with given length c
• Draw a circle around A with radius b
• Draw a circle with center point B and radius a
• Intersect the two circles to get the third triangle vertex C
• Draw the triangle ABC

The advantage of this DGS construction compared to one on paper is that you can vary the side lengths of the triangle dynamically. By changing the three sliders a, b and c we are able to examine a multitude of different triangles. Doing so, your students can easily find out that it's not always possible to construct a triangle for given side lengths. This observation can be the starting point for an interesting discussion about the triangle inequality.