2003 AMC 12B Problem 10

Below is the professionally curated solution for Problem 10 of the 2003 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 12B solutions, or check the answer key.

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Concepts:symmetry casework

Difficulty rating: 1490

10.

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?

$1$

$2$

$3$

$4$

$5$

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 $BC$ or $CD$ gives two figures; attaching it to $AE$ or $DE$ 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.

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