Students will explore the concept of geometric mean and solve right triangle problems using geometric mean proportions.
A TI-Nspire activity demonstrates interactively the geometric mean relationship, and an activity sheet applies the relationship to solve triangle problem. Most discussions of geometric mean related to right triangles are restricted to the length of the altitude as the mean between the parts of the hypotenuse determined by the point where the altitude intersects the hypotenuse.
Before the Activity
Download the attached TI-Nspire document (.tns file) and accompanying worksheet.
Students will need to install the .tns file on their calculators.
The students need to know how to write and solve a proportion.
With respect to right triangles, students should know what an altitude is; how to use the Pythagorean Theorem to find side lengths, and how segments are named.
For the TI-Nspire handheld, students should be able to grab a point and know how to use the measurement tool to measure length.
During the Activity
Students use the .tns file with their TI-Nspire calculators to see which sides and segments can be used to write proportions to solve right triangle problems.
The accompanying worksheet provides an opportunity for students to demonstrate that they understand and can apply the proportions to solve problems on their own.
Screens are interactive so that solutions to some problems vary according to the variations introduced by the student. Student will have to be able to grab a point to vary its location and to measure the length of a segment using the measurement tool.
After the Activity
Recommend instructor supplement the problems contained in the TI-Nspire document and worksheet with other multi-step problems that use both the Pythagorean Theorem and the geometric means of a right triangle determined by drawing the altitude to the hypotenuse.