Use the midpoint [icon]/images/ggb/toolbar/mode_midpoint.png[/icon] tool to find the midpoints of the three sides of the triangle.
Did you find the midpoints of the three sides?
Use the segment tool [icon]/images/ggb/toolbar/mode_segment.png[/icon]to connect each midpoint to the opposite vertex, constructing the medians of the triangles.
Where do the medians of the triangles intersect? ( Inside, outside or on a side of the triangle)
Does the point where the medians intersect change? ( Click on the [icon]/images/ggb/toolbar/mode_moverotate.png[/icon] before moving the vertices)
The [b]centroid[/b] is the point of intersection of the three medians of a triangle. [i]Write this in your notes![/i]
Place a point at the centroid of the triangle using the intersection [icon]/images/ggb/toolbar/mode_intersect.png[/icon] tool.
Can the centroid ever be located outside the triangle? Move the vertices around and see what happens before answering?
Did you place a point at the centroid?
Use the distance measurement tool [icon]/images/ggb/toolbar/mode_distance.png[/icon] to measure the lengths of the portions of the median from the vertex to the centroid, and then from the centroid to the opposite side. You should end up with 6 different lengths labeled on the diagram.
Do you have 6 different lengths labeled on the diagram?
What is the relationship between the distance from a vertex to the centroid and the distance the rest of the way from the centroid to the opposite side? If you don't see it immediately, try manipulating the vertices so that at least one of the lengths is a whole number.
What conclusion can you make about the relationship between the segments formed by the centroid and each median?