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Exploring
Centers of a Triangle: Part 2


 
Using problem solving skills,
formal geometry, and The Geometer’s Sketchpad, students will model and
solve a realworld problem by constructing the centroid of a triangle. Students will
explore further relationships of the medians of a triangle and investigate
how the centroid partitions each of the medians. Mathematics:
Students will investigate the medians of a triangle and the conjecture
the following theorems:
Extension activities include
investigating the Euler line for right, isosceles and equilateral
triangles. Mathematical
Thinking: Students will be
asked to predict, conjecture and
prove the aforementioned
theorems. Technology:
This activity uses several Sketchpad commands such as:
midpoint of a segment, polygon
interior, point at
intersection,
area, perimeter and distance.
The following sketch illustrates the use of the centroid to divide a triangle into three equal areas.


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