Education Technology

Geometry: The Geometric Mean

by Texas Instruments


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

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    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.

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    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.

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