Creating a Geometric Activity with GeoGebra

We will walk through the creation of an activity that explores the theorem from geometry that the three perpendicular bisectors of the sides of a triangle all meet in a single point.

Start by opening GeoGebra.

To create a triangle we first create three points. Select the new point icon from the menu bar.

Now click three times in the graph window to create points A, B, and C. Note that the coordinates of the points show up in the algebra window.

Now we want to add the line segments that make up the sides of the triangle. By clicking and holding the triangle at the bottom of the line icon, we turn it into a menu. We want to choose the item for segments through two points.

With the line segment tool chosen, we now select each vertex and then select the next vertex. This creates the sides. In the algebra window we the name of the segments and the length of each segment.

Similarly, we select the perpendicular bisector icon from the fourth menu and add in the bisectors of the three sides. In the algebra window we see the equation of each side.

For this applet, the axes are in the way. To unselect them, we click on the small triangle to the left of the graphics window to see the styling bar. If the selection tool (top icon, leftmost menu) is chosen this gives toggles to show or hide the axis and a grid in the view window.

The demonstration is ready first use. We can drag the vertices around and see that the bisectors all meet in a single point. We can drag the vertices around to see that this works for many examples.

Next we would like to add in structures that can be used to prove the theorem. We select the new point tool again and create a point on one of the bisectors.

Now we construct a circle with center on the bisector line and also going through a vertex on one end of the line bisected. (Select the highlighted tool, then select the point on the bisector, drag to the vertex. The circle is defined with center D and edge point B.) Note that the circle also hits the vertex on the other end of the edge.

When we move the vertex D to the point where the bisectors meet. The circle now goes through all three vertices.

Next we want to look at formatting. Be sure the styling bar is open. (Use the triangle next to Graphics at the upper left corner of the graphics window.) The options allow you to control color, line thickness and style, labeling, and locking properties.

Select segment a. drag the slider to change the line thickness to 3.

Choose the color tab and change the color to red.

Now select the copy visual style tool, then select lines a, b, and c in order to change the style of the other lines to match.

This highlights the triangle.

We would next like to modify the names of the edges and the bisectors. Control clicking on an object brings up a menu. We can either rename, or we can go to the object properties screen.

We want names that are easy to remember if we want to go back and edit. The segment connecting A and B gets renamed AB and its bisector BisectAB.

Using the styling bar we hide the label of the circle.

To improve the demonstration we would like to add a checkbox that hides or show the circle, with text that appears when the center is put in the right place. We choose the checkbox tool from the menu.

We set the checkbox to show or hide the circle and its center.

We need a we are done message

Use the intersection tool t put a point at the intersection of two bisectors.

We use the same menu to find the text tool.

We create the text we want the student to see when D reaches the intersection point.

We use the advanced tab to make the text appear only when the points are overlapping.

© Mike May, S.J., 2015