Problem:
Several figures can be made by attaching two equilateral triangles to the regular pentagon in two of the five positions shown. How many non-congruent figures can be constructed in this way?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
We may assume that one of the triangles is attached to side . The second triangle can be attached to or to obtain two non-congruent figures. If the second triangle is attached to or to , the figure can be reflected about the vertical axis of symmetry of the pentagon to obtain one of the two already counted. Thus the total is .
The problems on this page are the property of the MAA's American Mathematics Competitions