CCSS.Math.Content.8.G.A.1c
The standard
Parallel lines are taken to parallel lines.
Common Core State Standards for Mathematics
What this standard means
Students need to see that rigid motions keep parallel lines parallel. After a translation, rotation, or reflection, two lines that never met still never meet. They should be able to test this with tracing paper, a transparency, or geometry software, then explain what stayed the same.
Mastery looks like a student moving a pair of parallel lines and predicting the image before checking it. They can name the transformation and justify parallelism using equal slopes, equal distance apart, or matching angles. Students often get stuck when a rotation makes the lines look tilted, or when a reflection flips the picture and they think the relationship changed.
Ways to teach it
- Use patty paper to trace two parallel lines, rotate or flip the paper, and mark the new lines on grid paper.
- Ask students to explain why railroad tracks still appear parallel after turning a map upside down.
- Show three transformed line pairs on a grid and have students circle which original pairs must have been parallel.
- Look at road maps and identify streets that stay parallel after the map is rotated on a phone screen.
Plan a lesson for CCSS.Math.Content.8.G.A.1c
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Related standards
- CCSS.Math.Content.HSG-GPE.B.5
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicu...
- CCSS.Math.Content.8.G.A.1a
Lines are taken to lines, and line segments to line segments of the same length.
- CCSS.Math.Content.8.G.A.1b
Angles are taken to angles of the same measure.
- CCSS.Math.Content.HSG-SRT.A.1a
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.