####Right Triangle: Model for Exploring the Geometric Mean Theorem

The right triangle is one of the fundamental ideas in school mathematics. Among the numerous theorems about right triangles is the Geometric Mean Theorem, which states that the altitude (height) on the hypotenuse is the geometric mean of the two segments resulting from the altitude intersecting the hypotenuse. In other words, if we let h be the length of the altitude on the hypotenuse, m and n the lengths of the two segments, respectively, then h^2 = mn.

To make sense of the Geometric Mean Theorem, one needs to see the similarity between the two small right triangles created by the altitude, which is very confusing to some students -- h is to n as m to h or some alternative proportions. Some mental mapping needs to be in place. With the 3D printable model, one can physically align the triangles and see how the sides correspond to each other. Of course, all the three right triangles are similar, providing more opportunities for discussing similar triangles. The big triangle measures 60mm, 80mm, and 100mm on the inside.

References

1. https://en.wikipedia.org/wiki/Geometric_mean_theorem
2. http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/rightday3.html