standard_description: Prove the Laws of Sines and Cosines and use them to solve problems.
problem_activity: Narrative
In this activity, students create their own figures that have certain symmetry-based attributes. Students are given a pair of parallel segments on a grid. They then add more segments to create figures with one, two, and zero lines of symmetry.
To create their own figures, students rely on their understanding of symmetry and parallel lines. They consider where possible lines of symmetry could be, how many segments to add, and where to place them. They may also experiment, rely on familiar shapes and their lines of symmetry, or imagine a line of symmetry and what it would tell them about the figure. As they do so, they look for and make use of structure (MP7).
Action and Expression: Develop Expression and Communication.
Offer grid paper and copies of the pair of parallel line segments from the task. Invite students to use this paper to create multiple drafts, examining and refining their own thinking as they work.
Supports accessibility for: Conceptual Processing, Visual Spatial Processing, Organization
Required Materials
Materials to Gather
Straightedges
Launch
Groups of 2–4
Provide access to straightedges
Activity
2–3 minutes: independent work on the first question
2 minutes: group discussion
“Share your drawing for the first question. If needed, revise your thinking and drawing.”
5 minutes: independent work time on the remaining questions
3–5 minutes: group discussion
“Be sure to discuss how you know that your drawings have the specified number of lines of symmetry.”
Listen for attention to precision in students’ justifications. For instance, they may say the figure has line symmetry because:
the angles are the same
the sides have the same length and create the same angles when folded on top of each other
they measured all the parts and found them to be the same
they traced the figure and placed the copy on top of the original
Student Facing
Here is a pair of parallel segments that have the same length.
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Add one or more segments to create a figure with only 1 line of symmetry.
Here are two more pairs of parallel segments. Add more segments to make:
a figure with 2 lines of symmetry
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a figure with no lines of symmetry
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If you have time: Here are some other pairs of parallel lines. Add more segments to create a figure with 1 line of symmetry.
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Student Response
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Advancing Student Thinking
If students create figures with more or fewer lines of symmetry than planned, consider asking:
“How many lines of symmetry did you want your figure to have? How many lines of symmetry does it have?”
“How could you change your figure so it has fewer (or more) lines of symmetry?”
Activity Synthesis
Invite students to share their drawings and how they determined how and where to add segments.
“Which parts of the figure did you pay attention to when drawing? How did you make sure your drawing has line symmetry?“ (The segment lengths, angles, and distances from the line of symmetry all have to be the same on both sides of a line of symmetry.)
“What was tricky about creating figures with line symmetry in this task?” (Sample response: It was hard to figure out what to draw to get the exact number of lines of symmetry.)


aligns: no