Constructing a hyperbolic equilateral triangle in the Poincare disk

Back to Geometry homepage

Now use your hyperbolic ruler and compass tools to construct a hyperbolic equilateral triangle. Once you have done this then you should also be able to find the midpoint of two points.
The picture below contains an example of a hyperbolic equilateral triangle PQR with one side equal to PQ. The point M is the midpoint of PQ. Can you construct a hyperbolic equilateral triangle with one side equal to AB? Can you construct the midpoint of AB?
If you really understand Euclid's construction in Euclidean geometry then you should be able to easily do this in hyperbolic geometry using the hyperbolic line and hyperbolic circle tools that you have already constructed.

To help you get a feel for what the solution should be, there is already a tool for constructing hyperbolic equilateral triangles and hyperbolic midpoints. Try and construct them yourself, using only the other given tools.