Geometric Structures: Problem Set A (Triangles)

Prepared by:

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451


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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.