There is an equilateral triangle, , inscribed in a circle with center . What is the smallest angle you can rotate triangle around so that the image of is ?

Which segment is the image of when rotated  counterclockwise around point ?

5 segments on a grid, with Point P in the center. H I, horizontal, length 3, bottom left. F G, vertical, length 3, top left. On the right of F G, E D, slanting up and to the right. A B and B C, create right angle at B. A B, horizontal, length 3, top right. B C, vertical, length 3.

Here are 2 polygons:

Two congruent polygons on isometric grid labeled polygon P and polygon Q. Polygon P is above Polygon Q and shares common point A. Polygon P, beginning at bottom left and moving clockwise, the points are B, C, D, E, and A. Polygon Q, in corresponding order to Polygon P and moving counter-clockwise, the points are A, F, G, H, and J.

Select all sequences of translations, rotations, and reflections below that would take polygon to polygon .

1. Draw the image of figure when translated by directed line segment . Label the image of as , the image of as , and the image of as .
2. Explain why the line containing is parallel to the line containing .

A figure and directed line segment u. Figure made of two line segments A B and B C. A B slants upward and to the right, B C is horizontal. Segments meet at endpoint B, form angle A B C. Below and to the right of the figure, directed line segment u. Horizontal, no endpoint on left end, arrow at right end.

There is a sequence of rigid transformations that takes to , to , and to . The same sequence takes to . Draw and label :