Download Section 22.1

22.1
1.
An equilateral triangle in hyperbolic geometry has angles of measure 50 each. Find the
defect.
2.
Show why congruent triangles in hyperbolic geometry have equal areas. Is the converse
proposition true?
3.
Given the figure below. Calculate the defects of the four interior polygons. Test the validity
of the additive property of defects by calculating the defect of quadrilateral ABCD.
B
30
A
50
45
δ2
45
δ1
136
88
143
74
143
136
δ3
δ4
45
45
D
50
30
C
4.
The acute angle of a certain Lambert Quadrilateral (You may have to look this up.) has
measure of 83. Find its defect? What is the maximum defect of a Lambert Quadrilateral?
5.
The summit angles of a certain Saccheri Quadrilateral (You may have to look this up.) has
measure of 83. Find the defect of the quadrilateral. Why should the answer of this problem
be exactly twice as much as the answer to the previous problem?
6.
The defect of a certain regular dodecagon in hyperbolic geometry is 12. if O is the center,
find
a.
the measure of each angle of the polygon.
b.
The defect of the sub triangle ABO where O is the center and A and B are adjacent
vertices.
7.
Two regular pentagons have equal defects. Show they must be congruent.
8.
Show that if the defect of a regular pentagon is 90 then it can be used as a fundamental
region to tile the hyperbolic plane.