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Triangle
Centroid Patterns
Given
a triangle ABC. Construct on each side an equilateral triangle external
to triangle ABC.What happens when
you connect the centroids of the 3 equilateral triangles? Label this new
triangle DEF.
Repeat
the exercise, only this time; construct the equilateral triangles so that
they intersect the interior of triangle ABC. Let the centroids of these
three triangles be G, H, and I. What can you say about triangle GHI?
Compute
the area of triangle ABC, triangle DEF, and triangle GHI. Do you see any
relationship? (Hint: use Hero’s or Heron’s formula for finding the area
of a triangle)
Do
this experiment on at least 10 different triangles, showing all of your
construction work, and showing all of your data in a table. Make sure you
include a scalene triangle, an equilateral triangle, and isosceles triangle,
an isosceles right triangle, and an obtuse triangle, a right triangle,
and an acute triangle.
