Question

A triangle has rotation symmetry that can take any of its vertices to any of its other vertices. Select all conclusions that we can reach from this:

a. A rotation of 120° will map the triangle to itself.
b. All sides of the triangle have the same length.
c. All angles of the triangle have the same measure.
d. A rotation of 60° will map the triangle to itself.

Answer 1

Rotation symmetry of a triangle allows certain rotations to map the triangle to itself. All angles and sides of the triangle may not have the same measure, but rotations of 120° and 60° will map the triangle to itself. The correct conclusions are a and d

Step-by-step explanation:

A triangle with rotation symmetry means that you can rotate the triangle in such a way that one vertex can be mapped to any other vertex. From this, we can conclude the following:

1. A rotation of 120° will map the triangle to itself, so option a is correct.
2. All sides of the triangle do not necessarily have the same length, so option b is incorrect.
3. All angles of the triangle do not necessarily have the same measure, so option c is incorrect.
4. A rotation of 60° will map the triangle to itself, so option d is correct.

Therefore, the correct conclusions are a and d.