Equilateral Triangles in Poincare Disk
Now Lets Think About Equilateral Triangles
Remember: Euclidean Equilateral Triangles Have the Following Properties
- The angles in an equilateral triangle are all 60 degrees
- The sides in an equilateral triangle are all the same length
Below are two Triangles BDC and EFG
Just from looking at them, which triangle(s) do you think have equal interior angles? and Why?
Below are two Triangles BDC and EFG
Just from looking at them, which triangle(s) do you think have equal side lengths? and Why?
Now Lets Measure!
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: BDC or CDB)
Measure the Interior Angles
What is the sum of the interior angles in Triangle BDC?
Measure the Interior Angles
What is the sum of the interior angles in Triangle EFG?
What do you notice about Triangle BDC and EFG?
Did anything surprise you after measuring the interior angles?