In this lesson, you will use GeoGebra (file below) to construct the medians of a triangle. Directions: Step 1 Begin by selecting the point icon and placing three points, A, B, and C, on the drawing pad.
Step 2
Select the segment icon to create the segments between each pair of points. Note: You must click on the start vertex and then the end vertex to create a segment. To create AB , you must click on point A, then click on point B. Then, to create BC , you must click on point B again, then click on point C, etc., etc..
Step 3
Select the midpoint (or center) icon. Place the cursor over AB until it is highlighted (turns dark), then left-click on it. This should have created point D, the midpoint of AB . Likewise, create point E, (midpoint of BC ), and point F (midpoint of CA ).
Step 4
Select the segment icon, and construct (medians) AE , BF , and CD . If constructed properly, these three segments (medians) should intersect at a single point, called the centroid.
Step 5
Select the “point of intersection” icon. Place the cursor over the intersection of the three medians. When all three medians are highlighted (darkened), left-click and construct the centroid, (point of intersection). The centroid should be named G.
Step 6
Just for fun, left-click and drag either of the triangle vertices (points A, B, or C) around, verifying that the medians intersect at a point (always) and verifying that point G was constructed properly.
Step 7
Select the segment icon, and construct AG (from vertex A to centroid G). Next, construct GE (from centroid to midpoint opposite vertex A). Right click on either of these segments, bringing up the (object) properties menus. From within the “properties” dialogue box, click on the “show label” selector. To the right of this check-box, click on the drop-down menu and select “value”. The length of the segment will now be displayed dynamically (as things are changed). Click on segment h and this process, to display its length. Also, while in “properties”, you may increase the thickness and color of each of these segments. It’s slightly more appealing visually.
CONGRATULATIONS on your successful construction of medians.
Step 8
INVESTIGATE! Drag each vertex around to different coordinates. What is the relationship between AG and GE ?