The hexagon below contains diagonals that form six congruent triangles.

Question

The hexagon has 3 triangles on the top half and 3 triangles on the bottom half. Triangle A is at the bottom left, triangle B is at the top middle.

Which rotation about the center of the hexagon can be used to map onto ?

A.

60° clockwise
B.

120° clockwise
C.

180° clockwise
D.

240° clockwise

Answer 1

To determine which rotation about the center of the hexagon maps triangle A to triangle B, we need to consider the positions of the triangles within the hexagon.

Triangles are arranged such that:

• Triangle A is located at the bottom left position of the hexagon.
• Triangle B is at the top middle position of the hexagon.

The hexagon can be divided into 6 equal parts, with one triangle in each sector. Since the triangles are arranged like spokes on a wheel, we need to determine how many sectors we must move from triangle A to reach triangle B.

Here's how the counting of rotations works:

• Moving from position 1 (triangle A) to position 2 (next triangle) is a 60° rotation.
• Moving to position 3 is a 120° rotation.
• Moving to position 4 is a 180° rotation.
• Moving to position 5 is a 240° rotation.
• Moving to position 6 is a 300° rotation.

Since triangle A is in position 1 and triangle B is in position 4 directly across from triangle A, we have to move 180° clockwise to get from triangle A to triangle B.

Therefore, the correct answer is:

C. 180° clockwise