Lesson 8Rotation Patterns
Learning Goal
Let’s rotate figures in a plane.
Learning Targets
I can describe how to move one part of a figure to another using a rigid transformation.
Lesson Terms
- corresponding
- rigid transformation
Warm Up: Building a Quadrilateral
Problem 1
Using the right isosceles triangle, perform the following rotations:
Rotate triangle
degrees clockwise around . Rotate triangle
degrees clockwise around . Rotate triangle
degrees clockwise around .
What would it look like when you rotate the four triangles 90 degrees clockwise around
? 180 degrees? 270 degrees clockwise?
Activity 1: Rotating a Segment
Problem 1
Create a segment
Rotate segment
around point . Rotate segment
around point .
Construct the midpoint of segment
with the Midpoint tool. Rotate segment
around its midpoint. What is the image of A? What happens when you rotate a segment
?
Print Version
Rotate segment
180 degrees around point . Draw its image and label the image of as
Rotate segment180 degrees around point . Draw its image and label the image of as and the image of as . Rotate segment
180 degrees around its midpoint, What is the image of ? What happens when you rotate a segment 180 degrees around a point?
Are you ready for more?
Problem 1
Here are two line segments. Is it possible to rotate one line segment to the other? If so, find the center of such a rotation. If not, explain why not.
Activity 2: A Pattern of Four Triangles
Problem 1
Here is a diagram built with three different rigid transformations of triangle
Use the applet to answer the questions. It may be helpful to reset the image after each question.
Describe a rigid transformation that takes triangle
to triangle . Describe a rigid transformation that takes triangle
to triangle . Describe a rigid transformation that takes triangle
to triangle . Do segments
, , , and all have the same length? Explain your reasoning.
Print Version
You can use rigid transformations of a figure to make patterns. Here is a diagram built with three different transformations of triangle
Describe a rigid transformation that takes triangle
to triangle . Describe a rigid transformation that takes triangle
to triangle . Describe a rigid transformation that takes triangle
to triangle . Do segments
, , , and all have the same length? Explain your reasoning.
Lesson Summary
When we apply a 180-degree rotation to a line segment, there are several possible outcomes:
The segment maps to itself (if the center of rotation is the midpoint of the segment).
The image of the segment overlaps with the segment and lies on the same line (if the center of rotation is a point on the segment).
The image of the segment does not overlap with the segment (if the center of rotation is not on the segment).
We can also build patterns by rotating a shape. For example, triangle