Above is a general triangle in the Half-plane model of Hyperbolic Geometry. Line segments are arcs of circles centered on the Hyperbolic Half-plane Edge (x-axis) or they are vertical Euclidean line segments. The measure of an angle is given by the measure of the angle between Euclidean tangent rays. [br][br]What properties are shared by all Hyperbolic triangles?[br][br]Is the longest side always opposite the largest angle and the shortest side opposite the smallest angle?[br] [br]Investigate the sum of the measures of the interior angles. Is it pi = 180 degrees? Is it constant? If not, what range of values can the sum take on? Can you figure out what is meant by "defect"?