options: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Verify experimentally the properties of rotations, reflections, and translations:
- Lines are taken to lines, and line segments to line segments of the same length.
- Angles are taken to angles of the same measure.
- Parallel lines are taken to parallel lines.
problem_activity: Task
Find a way to partition a regular hexagon into 2 congruent figures. Explain how you know the 2 figures are congruent.
Find many ways to partition a regular hexagon into 2 congruent figures.
Find a way to partition a regular hexagon into 4 congruent figures. Explain how you know the 4 figures are congruent.
Find a way to partition a regular hexagon into 8 congruent figures. Explain how you know the 8 figures are congruent.
Bonus 1: Find a different way to partition a regular hexagon into 8 congruent figures.
Bonus 2: Find a different way to partition a regular hexagon into 4 congruent figures.
Bonus 3: Find yet another way to partition a regular hexagon into 8 congruent figures.


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