Triangles Inside The Poincare Disk
Recall some helpful information about Euclidean Triangles that may relate to our Hyperbolic Triangles
- The sum of the angles in a triangle adds up to 180 degrees
Please use the Applet Below for the Following Questions
Lets Make Some Hyperbolic Triangles
Start by constructing two lines
- Line AB
- Line CD
Now that we have our two triangles AEB and CED
Start by measuring the interior angles of our two triangles
USE THE ANGLE MEASURE TOOL
If an angle is not showing up, try clicking on the points in a different order (ex: AEB or BEA)
After Measuring the Interior Angles of our Triangles
What is the sum of the interior angles in Triangle AEB?
After Measuring the Interior Angles of our Triangles
What is the sum of the interior angles in Triangle CED?
Try Moving the Points Around
What happens to the angles as you move Points A, B, C, and D closer to the boundary of the disk?
Try Moving the Points Around
Can you find a triangle whose angles add up to 180 degrees?
Is this the same as Euclidean Triangles?
What are you noticing about Hyperbolic Triangles that is different from Euclidean Triangles?
Come up with one property you think Hyperbolic Triangles have
Collaborate with others if possible