Unit 1, Lesson 16
More Symmetry
Geometry
16.1
Warm-up
Which Three Go Together: Symmetry
Which three go together? Why do they go together?
A
B
C
D
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Which three go together? Why do they go together?
A
B
C
D
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?
A parallelogram inside two concentric circles, all with the same center. Bottom left vertex is on the outer circle. Top left vertex is on the inner circle. Top right vertex is on the outer circle. Bottom right vertex is on the inner circle.
A shape has rotation symmetry if there is a rotation greater than 0 degrees and less than 360 degrees that takes the shape to itself. A regular hexagon has many angles that work to create rotation symmetry. Here is one of them. What other angles would create a rotation where the image is the same as the original figure?
Can you think of a shape that has translation symmetry?
There aren’t any polygons with translation symmetry, but an infinite shape like a line can be translated such that the translation takes the line to itself.
A figure has rotation symmetry if there is a rotation that takes the figure onto itself. (This does not include rotations using angles, such as
This hexagon has rotation symmetry 60 degrees clockwise or counterclockwise around its center.
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