Triangles Inside The Poincare Disk

Recall some helpful information about Euclidean Triangles that may relate to our Hyperbolic Triangles[br][list][*][color=#38761d]The sum of the angles in a triangle adds up to 180 degrees[/color][/*][/list]

Please use the Applet Below for the Following Questions

Lets Make Some Hyperbolic Triangles

Start by constructing two lines[br][list=1][*]Line AB[/*][*]Line CD[/*][/list]

Now that we have our two triangles AEB and CED

Start by measuring the interior angles of our two triangles[br][br][color=#38761d]USE THE ANGLE MEASURE TOOL[br] If an angle is not showing up, try clicking on the points in a different order (ex: AEB or BEA)[/color]

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

Triangles Inside The Poincare Disk

Please use the Applet Below for the Following Questions

Lets Make Some Hyperbolic Triangles

Now that we have our two triangles AEB and CED

After Measuring the Interior Angles of our Triangles

After Measuring the Interior Angles of our Triangles

Try Moving the Points Around

Try Moving the Points Around

Is this the same as Euclidean Triangles?

Come up with one property you think Hyperbolic Triangles have

Information: Triangles Inside The Poincare Disk