Question

4 multiple answer 1 point a triangle has rotational symmetry that can take any of its vertices to any of its other vertices. select all conclusions that we can reach from this. all sides a triangle have the same length. all angles a triangle have the same measure. all rotations take one half of the triangle to the other half of the triangle.

Explanation:

Step1: Understand rotational - symmetry concept

A triangle with rotational symmetry that can map any vertex to any other vertex is an equilateral triangle.

Step2: Analyze side - length property

In an equilateral triangle, all sides are of equal length. Because of the rotational symmetry, the distances between vertices are equal, so all sides have the same length.

Step3: Analyze angle - measure property

In an equilateral triangle, all angles have the same measure. Since the triangle is symmetric under rotation, the angles between the sides must be equal, and each angle is 60 degrees.

Step4: Analyze the half - triangle property

The statement "All rotations take one half of the triangle to the other half of the triangle" is incorrect. Rotations of an equilateral triangle about its center map the whole triangle onto itself, not just one - half to the other - half.

Answer:

A. All sides a triangle have the same length, B. All angles a triangle have the same measure