GeoGebra Lab 9

Medians

1. Open your file called GeoGebra Altitude Lab. Hide the Altitudes. You should still have the intact triangle and the points Orthocenter and Circumcenter on your sketch as well as the midpoints.
2. A median of a triangle is a segment that connects a vertex to the midpoint of the side opposite it. Construct the medians of this triangle with the segment tool.
3. Construct the intersection of the medians. Remember to use the Intersect Two Objects tool. This is called the Centroid of the triangle. Right-click to rename this point ‘Centroid’.
4. Use the distance tool to measure the distance from the vertex end of one median to the centroid, the distance from the centroid to the midpoint end of that median, and the entire length of the median.
5. Save this sketch as GeoGebra Median Lab.

Answer the following questions in a textbox on your graphics view:

1. What can be said about the three medians of a triangle?
2. Do the properties that you observed for the orthocenter and the circumcenter hold true for this point? Test your conjecture by making the triangle right, obtuse, and acute.
3. Use a calculator to find the ratio of the length of the longer section of the median (vertex to centroid) to the total length.
4. Find the ratio of the length of the shorter section of the median (centroid to midpoint) to the total length.
5. What do these ratios tell you about the segments that are on the median? Does your conjecture hold true for the other medians?
6. Save this sketch as “GeoGebra Medians Centroid Theorem”