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.