Geometric Structures: Problem Set A (Triangles)
Prepared by:
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk/
1. Can you construct a triangle in the Euclidean plane which has edge lengths:
a. 1, 1, 1
b. 3, 3, 3
c. 3, 3, 1
d. 3, 1, 1
e. 6, 5, 4
f. 9, 5, 4
g. 5, 4, 3
h. 10, 8, 6
i. Can you state a general "theorem" which tells when three real numbers a, b, c are the edge lengths of a triangle in the Euclidean plane.
j. For each triangle you were able to construct in parts a - f how would you describe the triangle that you obtained.
k. Repeat each of the parts of the question above but this time for a triangle in the Taxicab plane.