Lesson Designed By:

Janet Mae Zahumeny
Roselle Park High School
e-mail: 74620.2745@compuserve.com

TOPIC:

The Centroid of a Triangle

LEVEL:

Secondary Plane Geometry

GEOMETER'S SKETCHPAD PROFICIENCY:

Beginner / Intermediate

CLASS TIME:

1 class period (42 minutes)

GEOMETER'S SKETCHPAD SKILLS NEEDED:

Students should be familiar with the CONSTRUCT and MEASURE menus, and should know how to use the Sketchpad CALCULATOR.

NOTES TO TEACHER:

To begin this activity students should be familiar with the terms centroid and median, or have access to a dictionary or geometry book.

This investigation is an extension of one found in Exploring Geometry with The Geometer's Sketchpad, which gives detailed directions on the construction of a centroid and an investigation of the ratios of the segments formed on the medians.

*** See the v3 Review for more information on Sketchpad activity books. ***

ACTIVITY: THE CENTROID OF A TRIANGLE

PROCEDURE

1. Draw a triangle and construct the centroid.

2. Shade in each of the small triangles a different color.

3. Which, (if any) of these small triangles appear to have equal areas?

4. Measure the areas of all 6 small triangles.

  • Change the size and shape of the original triangle.
  • Does the relationship of the areas change?
  • Was your conjecture for #3 correct?
  • Were your surprised? Why (or why not)?

5. What do you think is true about the perimeters of the 6 triangles?

6. Measure their perimeters.

  • Was your conjecture correct?
  • Were you surprised? Why (or why not)?

7. What can you say about the areas and perimeters of triangles?

  • Do any of the numbered triangles appear to be congruent?

9. Show that ONE PAIR of the small triangles is (or is not) congruent.

  • Explain what you did!!!