Construction of Centroids

By

Cassian Mosha

1.The CENTROID (G) of a triangle is the common intersection of the three medians. A median of a triangle is the segment from a vertex to the midpoint of the opposite side.

Use Geometer's Sketchpad (GSP) to Construct the centroid and explore its location for various shapes of triangles.

Solution:

First draw a triangle ABC as shown below

Triangle 1

Then find the mid points of every segment, that is segment AB, BC, and CA

Triangle 2

Then construct the segments connecting the mid points and the vertices of the triangle

Triangle 3

The intersection of the three points named G is the centroid of triangle ABC. Now we will try to construct few triangles of different shapes and see where the centroid lies. We can hypothesize  that centroids of all triangles lies inside the triangle.

Triangle 4

With this triangle we see that the centroid also fall inside the triangle of angles measure

LetŐs also try a right angled triangle and see what will happen.

Triangle 5

As we can see the centroid still is inside the right-angled triangle, and we can conclude the above statement that the centroid of any triangle no matter what shape it my have will lie inside the triangle.

LetŐs do one more triangle with two acute angles and one obtuse triangle to solidify our conclusion.

Triangle 6

The intersection pint G is still inside even though the triangle had n obtuse angle of  and the acute angles both having each. The centroid of any triangle lies inside the triangle, and this affirms the above theorem.

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