Unit 1, Lesson 8
Moves in Parallel
Accelerated 7
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In this Warm-up, students practice applying rigid transformations to lines. Each image in this activity has the same starting line and students name the translation, rotation, or reflection that takes this line to the second marked line. Because of their infinite and symmetric nature, different transformations of lines look the same unless specific points are marked, so 1–2 points on each line are marked.
While students have experience transforming a variety of figures, this activity provides the opportunity to use precise language when describing transformations of lines while exploring how sometimes different transformations can result in the same final figures. During the activity, encourage students to look for more than one way to transform the original line.
Provide access to tracing paper. Give students 2 minutes of quiet work time followed by whole-class discussion.
For each diagram, describe a translation, rotation, or reflection that takes line
Then plot and label
Invite students to share the transformations they chose for each problem. Each diagram has more than one possible transformation that would result in the final figure. If students only found one, pause for 2–3 minutes and encourage students to see if they can find another. For the first diagram, look for a single translation, single rotation, and single reflection that work. For the second diagram, look for a single rotation and a single reflection.
MLR1: Stronger and Clearer Each Time
To Gather
Tracing paper
In this activity, students investigate what happens to parallel lines under rigid transformations by performing three different transformations on a set of parallel lines.
Students recall that parallel lines do not meet, and they remain the same distance apart. Students use the structure of rigid transformations to observe that the image of a set of parallel lines after a rigid transformation is another set of parallel lines (MP7).
Display this question for all to see, then read it aloud for the class: “What happens to parallel lines when we perform rigid transformations on them?” Tell students they will investigate this question, and leave it displayed throughout the activity.
Arrange students in groups of 3. Provide access to tracing paper. Assign one problem to each member of the group. Give 3–5 minutes of quiet think time, then have students share their findings with their groups.
Use a piece of tracing paper to trace lines
As you perform each transformation, think about the question:
What is the image of two parallel lines under a rigid transformation?
Translate lines
Rotate lines
What is the same in the original and the image?
Reflect lines
Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to “What happens to parallel lines when we perform rigid transformations on them?” In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help their partner clarify and strengthen their ideas and writing.
If time allows, display these prompts for feedback:
Close the partner conversations and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer.
Provide these sentence frames to help students organize their thoughts in a clear, precise way:
Here is an example of a second draft:
Performing a rigid transformation on a set of parallel lines results in another set of parallel lines because the distances and angles will stay the same between the original set and its image. The new lines won’t always be parallel to the original lines, since they could have been rotated. A reflection will sometimes result in a set of lines parallel to the first one, and a translation will always result in a set of lines to the first one, since angles stay the same in a translation.
As time allows, invite students to compare their first and final drafts. Select 2–3 students to share how their drafts changed and why they made the changes they did.
Sometimes, a rigid transformation takes a line to itself. For example:
A line, labelled M. Points A, B, F, B prime and A prime are labelled on the line. A line of reflection intersects the line at point F and is perpendicular to the line M.
These facts let us make an important conclusion.
If two lines intersect at a point, which we’ll call
Rotating both lines by
Help us improve by sharing suggestions or reporting issues.
Students may not perform the transformations on top of the original image. Ask these students to place the traced lines over the original and perform each transformation from there.
On the diagram, draw the image of the line and points
Label the images of the points
What is the order of all seven points? Explain or show your reasoning.
Rotate the figure
What do you know about the relationship between angle
Rotate the figure
What do you know about the relationship between the angles in the figure? Explain or show your reasoning.
In the second question, students may not understand that rotating the figure includes both segment