Centroid and Orthocenter

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Geometry: Triangles

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-84 series

Applications

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Other Materials

This is Activity 7 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

Resource Types

Lessons

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Centroid and Orthocenter

Activity Overview

In this activity, students analyze the location of the centroid and orthocenter for different triangles.

Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

TI-Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable

TI-Navigator™ "send to class" feature

See the attached PDF file for detailed instructions for this activity

Print pages 27 - 29 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Construct an acute triangle and label its vertices

Construct medians and notice that all medians intersect in a point, called the centroid

Determine the location of the centroid

Alter the triangle by dragging one of the vertices around the screen to create an obtuse triangle

Determine the location of the centroid

Alter the triangle to create a right triangle

Determine the location of the centroid

Note that for all triangles, the centroid lies inside the triangle

Create an acute angled triangle and construct its altitudes

Note that all altitudes of a triangle have only one point of intersection, called the orthocenter

Determine the location of the orthocenter

Identify that when the triangle is acute, the orthocenter lies inside the triangle

Alter the triangle to create an obtuse angle

Observe that when the triangle is obtuse, the orthocenter lies outside the triangle

Alter the triangle to create a right angle

Observe that the orthocenter lies on the triangle

After the Activity

Review student results:

As a class, discuss questions that appeared to be more challenging

Re-teach concepts as necessary

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix A PDF Teacher Notes Appendix B PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Geometry: Triangles

Level

9-12

Activity Time

60 Minutes

Software

TI Connect™

TI Calculator

TI-84 series

Applications

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Other Materials

This is Activity 7 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

Resource Types

Lessons

Report an Issue

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Centroid and Orthocenter

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

Centroid and Orthocenter

Before the Activity Files

Cabri™ Jr. for TI-83 Plus and TI-84 Plus

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