In hyperbolic geometry, do all triangles have incenters? How about
circumcenters, othrocenters, and centroids?
You probably noticed in Activity 9-3(3) that either all three altitudes
intersect through a single point, or else none of them intersect at
all. Is this true also with angle bisectors, perpendicular bisectors of
sides, and medians? (Challenge problem: can you prove any of this?)
Does the Parallel Projection Theorem hold in hyperbolic geometry? Explain
why.
Do there exist similar non-congruent triangles in hyperbolic geometry?
Explain why.
Given an angle, bisect it without using the "Bisect Angle" menu
option in the non-Euclid Applet.
Given a line segment, construct its perpendicular bisector without using
the "Plot Midpoint" and the "Draw Perpendicular" menu
options in the non-Euclid Applet.
Given a circle C and a point P outside the circle, construct (using the
non-Euclid Applet) a line through P tangent to C. You may not use the
Constructions menu options "Draw segment of specific length" and
"Draw ray at specific angle".