What and Why

Author:
Bob Allen
1. Construct segment AB. 2. Construct a circle with center A and radius AB. 3. Construct a circle with center B and radius BA. 4. Pick one point of the points of intersection and name it C. 5. Construct triangle ABC.

Click and drag point A around. Click and drag point B around. Did your sketch break?

Check all that apply
If you answered yes, make the sketch again. Engage help. If no, please continue.

What kind of triangle did you create?

How do you know? What did you measure? Are the measurements on your sketch? If not, please include them.

Now, how do you know this will work every time? Imagine a segment AB the size of the galaxy. Or imagine segment AB the size of a molecule. Convince me that you will always get the type of triangle you identified. Hint: You made three circles. How do segments AB, AC, and BC relate to each other and those circles? What are they?