**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.