The definition of isosceles triangle can determine whether an equilateral triangle is a special case of an isosceles triangle. Using the Cabri Jr. application, students can get a feel for which definition makes the most sense. Along the way, they get experience with a perpendicular bisector, measuring lengths, and an informal look at the intermediate value theorem.
Before the Activity
Prior to beginning this activity, students need to be familiar with how Cabri Jr. operates.
During the Activity
Start the Cabri Jr. application with a new sketch. Use the Segment tool to draw a segment near the bottom of the screen.
Next, use the Perp. Bis. tool to construct the perpendicular bisector of the segment previously drawn.
Use the Point on tool to place a point on the perpendicular bisector.
Use the Hide/Show tool to hide the perpendicular bisector, but not the point on the bisector. Then use the Segment tool to connect the visible point to the endpoints of the original segment.
Use the Measure tool, option D. & Length, to measure the lengths of the three edges of the triangle. After getting the length of an edge, depress the + key to get a second decimal place in the length?s value. Move those lengths to convenient places on the screen. Have the students discuss what kind of triangle is shown. You may want to have them explain why that is true in this situation.
After the Activity
If you want to avoid this discussion, you can keep the number of decimal places in the lengths to be one. In that way, it is quite likely that, to one decimal place, the edge lengths will be equal. In my experience, however, it is healthy to talk about the situations that often arise with two decimal place accuracy.
After the work on the calculator, you can pose the questions ?At what point did the isosceles triangle become equilateral?? ?Did any of the triangle?s fundamental properties change, i.e., number of edges, straightness of its edges, etc.?? Do you think an equilateral triangle is a special case of an isosceles triangle??