IM Geo.1.16 Lesson: More Symmetry
Which one doesn’t belong?
A:
B:
C:
D:
Determine all the angles of rotation that create symmetry for the shape your teacher assigns you. Create a visual display about your shape. Include these parts in your display:
- the name of your shape
- the definition of your shape
- drawings of each rotation that creates symmetry
- a description in words of each rotation that creates symmetry, including the center, angle, and direction of rotation
- one non-example (a description and drawing of a rotation that does not result in symmetry)
Finite figures, like the shapes we have looked at in class, cannot have translation symmetry.
But with a pattern that continues on forever, it is possible. Patterns like this one that have translation symmetry in only one direction are called frieze patterns. What are the lines of symmetry for this pattern?
What angles of rotation produce symmetry for this pattern?
What translations produce symmetry for this pattern if we imagine it extending horizontally forever?
Clare says, "Last class I thought the parallelogram would have reflection symmetry. I tried using a diagonal as the line of symmetry but it didn’t work. So now I’m doubting that it has rotation symmetry."
Lin says, "I thought that too at first, but now I think that a parallelogram does have rotation symmetry. Here, look at this."
How could Lin describe to Clare the symmetry she sees?