Question

practice 2
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.
a all sides of the triangle have the same length.
b all angles of the triangle have the same measure.
c all rotations take one half of the triangle to the other half of the triangle.

Explanation:

• For a triangle to have rotational symmetry that maps any vertex to another, it must be an equilateral triangle. In an equilateral triangle, all sides are equal (by definition of an equilateral triangle).
• Also, in an equilateral triangle, all angles are equal (each angle is \(60^{\circ}\) since the sum of angles in a triangle is \(180^{\circ}\) and \(180\div3 = 60\)).
• Rotational symmetry of order 3 (as in an equilateral triangle) does not mean that all rotations take one - half of the triangle to the other half. A rotation of \(120^{\circ}\) (the non - identity rotational symmetry of an equilateral triangle) does not split the triangle into two equal halves in that sense.

Answer:

A. All sides of the triangle have the same length.

B. All angles of the triangle have the same measure.