This is the first tutorial in the Geometer’s Sketchpad Essentials (GSP) Series. In this tutorial, we are going to investigate the medians of a triangle. We will learn how to use the basic tools: *Point Tool*, *Selection Arrow Tool*, and the *Segment Tool*. If you are not familiar with GSP, you may want to read Introduction to Geometer’s Sketchpad.

The output of our tutorial is shown in the Figure above; points *D*, *E*, and *F* are midpoints of the sides of triangle *ABC*.

** Instructions**

1.) Open Sketchpad.

2.) Select the **Point tool** and click three different locations on the drawing area or *sketch pad*.

3.) Select the **Text tool** and click all the points one by one to display their labels. Notice that GSP labels the points in alphabetical order.

4.) Next, to construct segment *AB*, click the **Segment tool** (second figure), click point *A* and then click point *B*. The small arrow at the lower-right of the** Segment tool** indicates that there are other tools in that box. You can view these tools by clicking on that tool and holding the mouse button. The **Segment tool** is one of the tools in the **Straightedge toolbox**. The Selection Arrow tools are also shown in the figure below.

5.) With the **Segment tool** still selected, construct segments *BC* and AC.

6.) To familiarize yourself with how dragging works in GSP, click the **Selection tool** (the Translate arrow) and drag the vertices, segments, and labels of the triangle. To drag the whole object, drag the across the entire construction to highlight all the objects, and then drag one of the objects. Now try the other two selection arrows and observe what happens.

7.) To construct the midpoint, click segment *AB* (be sure that no point is selected), click the **Construct** menu from the **Menu bar**, and then click **Midpoint**.

8.) Now, to construct the midpoints of *BC* and *AC*, select both segments (again with no point selected), click the **Construct** menu, and then click **Midpoints**.

9.) Now, to label the midpoints, select the text **Text** tool and then click the midpoints of *AB*, *BC*, and *AC* in that order.

10.) Next, select the **Segment tool**, and then construct *AE*, *BF* and *CD*. These segments are the median of the triangle. A median of a triangle is a segment connecting the vertex to the midpoint of the opposite side.

11.) Use the **Selection Arrow tool** and move the vertices and segments of the triangle. What do you observe? Make a conjecture about your observation.

12.) Click **File>Save**, and type centroid as the file name construction. We will need this construction in later tutorials.