Question

2 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 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. 3 select all the angles of rotation that produce symmetry for this flower. a 45° b 90° c 135° d 180° e 225° f 270°

Explanation:

Step1: Analyze triangle rotation symmetry

If a triangle has rotation symmetry that can take any vertex to any other vertex, it is an equilateral triangle. In an equilateral triangle, all sides are equal and all angles are equal.

Step2: Evaluate option C

Rotations in an equilateral - triangle do not divide it into two equal - halves in the sense described in option C. A rotation that takes one vertex to another does not split the triangle into two congruent sub - triangles in that way.

Step3: Analyze flower rotation symmetry

For the flower, if we assume it has 8 - fold rotational symmetry (by counting the number of "petal - like" or repeating elements), the angles of rotation that produce symmetry are given by $\frac{360^{\circ}}{n}$, where $n$ is the number of times the figure coincides with itself during a full 360 - degree rotation. Here $n = 8$, and $\frac{360^{\circ}}{8}=45^{\circ}$. So, rotations of $45^{\circ},90^{\circ},135^{\circ},180^{\circ},225^{\circ},270^{\circ}$ will produce symmetry.

Answer:

1. A. All sides of the triangle have the same length; B. All angles of the triangle have the same measure
2. A. $45^{\circ}$; B. $90^{\circ}$; C. $135^{\circ}$; D. $180^{\circ}$; E. $225^{\circ}$; F. $270^{\circ}$