2003 AMC 12B Problem 10

Problem 10 of 25Easier

Several figures can be made by attaching two equilateral triangles to the regular pentagon

ABCDE

in two of the five positions shown. How many non-congruent figures can be constructed in this way?

Show solution

Solution

Assume one triangle is attached to side

AB.

The second triangle can be attached to a side that is one step away or two steps away from

AB.

Attaching it to

BC

CD

gives two figures; attaching it to

AE

DE

gives figures that are mirror images of these across the pentagon’s axis of symmetry. So there are only

2

non-congruent figures. Thus, the correct answer is B.