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 triangle A onto triangle B?

A.
60° clockwise

B.
120° clockwise

C.
180° clockwise

D.
240° clockwise

Answer 1

To determine the rotation that maps triangle A (bottom left) to triangle B (top middle) in a hexagon, we need to analyze the positions of the triangles.

The triangles are positioned as follows:

• Triangle A is at the bottom left.
• Triangle B is at the top middle.

In a hexagon, rotating the figure involves the angles between adjacent vertices. A regular hexagon can be divided into six equal sections, each corresponding to a rotation of \(60^\circ\).

We can calculate the positions based on these angles:

1. Starting from triangle A (at a position of 0 degrees):
   • 60° clockwise: Moves to the bottom right triangle.
   • 120° clockwise: Moves to the top right triangle.
   • 180° clockwise: Moves to the top middle triangle.
   • 240° clockwise: Moves to the top left triangle.

From our observations:

• A rotation of 180° clockwise would move triangle A directly to the position of triangle B (top middle).

Thus, the answer is:

C. 180° clockwise.