back home

GeoGebra Lab 12

The Triangle Exterior Angle Theorem

  1. Open GeoGebra and draw an arbitrary \(\angle ABC\). It’s helpful to turn off the Axes and Grid so that your drawing space is cleaner.

  2. Using the Ray tool in the Segment toolbox, click on first point \(A\), then point \(B\). This will extend side \(AB\) past \(B\).

    GeoGebra screen capture
  3. Place a point, \(D\), on ray \(AB\) past \(B\) so that \(B\) is between \(A\) and \(D\). The Point on Object tool in the Point toolbox is helpful to make sure that \(D\) is on ray \(AB\).
  4. Measure \(\angle CBD\). This is called an exterior angle of this triangle. Also measure \(\angle CAB\) and \(\angle BCA\) which are called the remote interior angles to \(\angle DBC\). Why do you think these angles are named this way? If any of your angles is larger than 180°, right click the angle and in the Settings, in the Basic tab, select “Angle Between 0° and 180°”
  5. You will use the Input bar (at the bottom of the Algebra view window) to create a measurement that is the sum of these two angle measures. First, find the first remote interior angle on the Algebra view. Right click it and rename it p (so that you do not have to deal with the Greek letter assigned it). Rename the other remote interior angle as q and the exterior angle as e. Then, in the input bar, type: sum = p + q.

  6. Create a text box. In the box, type Exterior Angle =, then click on the “Advanced” drop-down under the typing area. Choose the tab with the GeoGebra icon (shown below), which provides a list of objects that exist in your GeoGebra page. From this list, select “e”, the name of your exterior angle. The preview of your text will show up in the bottom of the window. Finally, click OK to close the text box window.

    GeoGebra tab
  7. Create another text box and type Sum of Remote Interior Angles =. Using the same process as in step F, select sum from the list of Objects.
  8. Drag one of the vertices of the triangle. What do you observe?
  9. What do you think the relationship between the exterior angle and one remote interior angle would be if this were an isosceles triangle with a base AC? Why?
back home