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Exploring the Geometric Means of a Right Triangle - When the Altitude to the Hypotenuse Is Drawn

Author
Paul Trogdon
Alignment
Standards Alignment
Textbook Alignment
Subject Area
Math: Geometry: Similarity and Proportion
Math: Geometry: Triangles
Level
9-12
Activity Time
50 Minutes
TI Calculator
TI-Nspire™ CX series
TI-Nspire™ CX CAS/CX II CAS
TI-Nspire Version
3.0
Other Materials
Geometry_GeometricMean_Trogdon.tns is the document to be used on either TI-Nspire or TI-Nspire CAS technology. There is a accompanying notetaking document to go with the activity.
Resource Types
Lessons
Format
TNS
Report an Issue

Exploring the Geometric Means of a Right Triangle - When the Altitude to the Hypotenuse Is Drawn

Activity Overview

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.

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    Download Files
    During the Activity Files
    Student Activity DOC TI-Nspire Activity TNS
    Author
    Paul Trogdon
    Alignment
    Standards Alignment
    Textbook Alignment
    Subject Area
    Math: Geometry: Similarity and Proportion
    Math: Geometry: Triangles
    Level
    9-12
    Activity Time
    50 Minutes
    TI Calculator
    TI-Nspire™ CX series
    TI-Nspire™ CX CAS/CX II CAS
    TI-Nspire Version
    3.0
    Other Materials
    Geometry_GeometricMean_Trogdon.tns is the document to be used on either TI-Nspire or TI-Nspire CAS technology. There is a accompanying notetaking document to go with the activity.
    Resource Types
    Lessons
    Format
    TNS
    Report an Issue
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