Download 3.4 Congruence in Hyperbolic Space

3.4 Congruence in the hyperbolic plane
Theorem: If three angles of one triangle are congruent respectively to three angles of
another triangle, the triangles are congruent (AAA congruence).
Note: In the hyperbolic plane, you cannot have similarity without congruence.
Theorem: Saccheri quadrilaterals with congruent summits and summit angles are
congruent.
Theorem: Two omega triangles are congruent if the sides of finite length are congruent
and if a pair of corresponding angles not located at the omega points are congruent.
Theorem: Two omega triangles AB and AB   are congruent if A  A and
B  B  .
Exercises
1.
Given omega triangles AC and BC with AC  CB , is AC  BC .
Justify.
2.
If the angles with ordinary vertices in an omega triangle are congruent, then the
line from the omega vertex to the midpoint of the opposite side is perpendicular to that
side.
3.
Is AAAA is a congruence condition for quadrilaterals in hyperbolic space?
4.
Find the flaw in the proof of exercise # 5. page 130.