Medians of a Triangle
Directions
Discover the Relationship between Median, Centroid and the Given
Triangle
What is the Median of
a Triangle?
A median of a triangle is the line segment that joins any
vertex of the triangle with the midpoint of the opposite side.
1. Explore the commonly known triangles
(Equilateral, Isosceles, Acute, Obtuse)
Pick at least one of the commonly
known triangles to explore.
Using the tools provided,
construct one median on the triangle and make a conjecture about what a median
does to a triangle. Explain your conjecture.
How many medians can you create in
a given triangle? Why?
Click the checkbox for the
triangle you chose. This will show the remaining medians. Make a conjecture
about what happens to a triangle when all medians are constructed. Use the
tools provided to support your conjecture.
What is the Centroid
of a Triangle?
A centroid of a triangle is the point where the three
medians of the triangle meet.
Make a conjecture about the relationship the centroid has with each of the medians. Use
the tools provided to support your conjecture.
2. Explore the Transformable Triangle
Using the tools provided,
construct all the medians and the centroid on the transformable triangle.
Do your conjectures hold true?
What if you move the vertices of the triangle?