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Review
The median of a triangle is a line that passes through a vertex and the midpoint of the opposite side of the triangle. The three medians intersect at one single point called the centroid.(see figure 1 below).
Below, an applet is used to explore the definition and properties of the medians of a triangle.
Tutorial
1 - click on the button above "click here to start" and MAXIMIZE the window obtained.
2 - Change the position of the vertices of the triangle and note that the three medians are concurrent at the centroid O.
3 - Change the positions of the vertices so that triangle ABC is an isosceles triangle. Use the squares of the grid to have length of side AB equal to the length of side AC.(see figure 2 below).
Question: Show that triangles ABP and ACP are congruent and angles APB and APC are right angles.
4 - Change the positions of the vertices and note and compare the distances from any vertex to the centroid O and the distance from O to the midpoint of the opposite side to the vertex. All these distances are displayed on the applet panel.
More
Geometry Tutorials, Problems and Interactive Applets.
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