Right Triangles in the Poincare Disk

Recall some helpful information about Euclidean Right Triangles that may relate to Hyperbolic Right Triangles

[list][*][color=#38761d]The right angle is 90 degrees[/color][/*][*][color=#38761d]The Pythagorean Theorem: [math]a^2+b^2=c^2[/math][/color][/*][/list]

Using the Side Lengths From The Triangle AEB Above

[math]a=1.8[/math], [math]b=1.84[/math], [math]and[/math] [math]c=3[/math][br]Compute [br][list][*][math]a^2+b^2[/math][math],and[/math][br][/*][*][math]c^2[/math][br][br][/*][/list]

Using the Side Lengths From The Triangle CED Above

[math]a=1.64[/math], [math]b=1.8[/math], [math]and[/math] [math]c=2.81[/math][br]Compute [br][list][*][math]a^2+b^2[/math][math],and[/math][br][/*][*][math]c^2[/math][br][br][/*][/list]

Use This Area to Discuss What You Are Noticing About the Triangles Above

Here are some prompts to help with your response:[br][color=#0000ff] - Does [/color][math]a^2+b^2=c^2[/math][color=#0000ff]?[br] - If you move the points around, are you able to find an a, b and c value that make the statement true?[br] - If not, what do you notice about the relationship between [/color][math]a^2+b^2[/math][color=#0000ff] versus [/color][math]c^2[/math][color=#0000ff] ?[/color]

Right Triangles in the Poincare Disk

Recall some helpful information about Euclidean Right Triangles that may relate to Hyperbolic Right Triangles

Using the Side Lengths From The Triangle AEB Above

Using the Side Lengths From The Triangle CED Above

Use This Area to Discuss What You Are Noticing About the Triangles Above

This Space is to Illustrate Your Thinking (If Needed)

Information: Right Triangles in the Poincare Disk