Setup (Behind the Scenes)
Draw a quick triangle using the software and display each side length and angle measure. These will adjust as a vertex is dragged. Here are shots to show you how it looks in GeoGebra. The triangle/shape button is first, then use the angle measure button to mark off the three points that name each angle. (Do 3 times to get all 3 angles marked.)
The Lesson - Phase 1:
Ask the first student to drag a vertex to make the triangle a right triangle. He or she will drag a vertex and move things around until they can get one angle measure to be 90 degrees. Success! Then have another student come up. The kids love this, and are so excited to play with the geometry software for the first time.
Calling up one student at a time, have them create a few basic types of triangles (something like an acute isosceles triangle, and then an obtuse isosceles triangle, and then even a right isosceles triangle).
Once you have been through a few of these successfully, give the next student a challenge to create a "right equilateral" triangle. Do not hint that it cannot be done. Some students may figure out that it is impossible after just a minute and giggle as the student tries dragging a vertex different ways.
Eventually, you can allow them to explain why they think the student at the board should give up. Continue on with some possible and some impossible triangles.
Request the following triangles:
- right isosceles
- obtuse scalene
- obtuse equilateral
- right obtuse
This leads to really great discussions. As an extension, you can have students list as many impossible triangles as they can. Let your class explore and investigate triangles using the software. Allow students to explain WHY certain triangles are impossible.
The Lesson - Phase 2:
Try other hands-on activities exploring triangle sum theorem. One option is to have students draw a large triangle, rip off all three vertices, and line them up in a row.
Join together as a whole class to discuss and make sure that all pairs understand.