• • • ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• TI-84 Plus C Silver Edition
• TI-84 Plus CE
• ##### Software

TI Connect™
TI Connect™ CE

# Geometry: The Geometric Mean

by Texas Instruments #### Overview

In this activity, students will establish that several triangles are similar and then determine that the altitude to the hypotenuse of a right triangle is the geometric mean between the segments into which it divides the hypotenuse.

#### Key Steps

• In Problem 1, students use the Cabri™ Jr. App to construct a right triangle with an altitude from the right angle to the hypotenuse. Then, they measure the altitude and the segments of the hypotenuse.

• Students calculate the geometric mean by using the Text and Calculate tools to find the product of the two segments and the square of the altitude. They drag a vertex of the triangle and observe the changes.

• Students change their figure by dragging the vertices. They use the geometric mean of the triangle to estimate the radical values.