Triangles

From the tools we have already constructed you can start to study the Hyperbolic Geometry. One of the most interesting aspects to study are the properties of the hyperbolic triangles.

Remember that the sum of the angles of a triangle is always less than two right angles and that there are not similar hyperbolic triangles, that is, fixed the angles of a triangle the lengths of the sides will be fixed. This is consequence of the relationship among lengths and angles that the formula of the angle of parallelism gives us.

It is interesting to study the remarkable points of a hyperbolic triangle. In order to see when they exist we created the tools that allow us to construct some of the points and remarkable straight lines.

- Hyperbolic triangle,

- Hyperbolic equilateral triangle (if the angle is fixed, it is unique),

- Hyperbolic circumcenter,

- Circumscribed circumference,

- Barycenter,

- Hyperbolic Incenter,

- Incircle,

- Excenter,

- Excircles and

- Orthocenter.

 
To obtain the macros, if you have the Sketchpad 4.05 installed you can download Hyperbolic Triangles.gsp.

Hyperbolic geometry
Main page