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Geometry Lesson

Rigid Transformations: Preserving Shape, Changing Position

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High SchoolThin-SlicingCCSS.MATH.CONTENT.HSG.CO.A.2, CCSS.MATH.CONTENT.HSG.CO.A.4, CCSS.MATH.CONTENT.HSG.CO.B.650 min
Learning Objective

Students will be able to apply translations, reflections, and rotations to figures on the coordinate plane, describe transformations using precise notation, and justify why rigid transformations preserve congruence.

Lesson Overview

Students progress from identifying coordinates after a single translation to composing multiple rigid transformations and justifying congruence, changing exactly one variable of complexity at a time across six tasks.

Materials

  • Vertical whiteboards or chart paper
  • Dry-erase markers (multiple colors)
  • Rulers
  • Protractors
  • Random grouping tool
  • Printed coordinate grids (backup)

Scaffolded Task Progression

1Task 1
Triangle $ABC$ has vertices $A(1, 2)$, $B(4, 2)$, $C(4, 5)$. Translate the triangle $5$ units right and $3$ units down. Write the coordinates of $A'$, $B'$, and $C'$. Plot both triangles on the grid. ```coordgraph {"title":"Task 1 — Translation","xLabel":"x","yLabel":"y","xRange":[-1,11],"yRange":[-3,8],"xStep":1,"yStep":1,"polylines":[{"points":[[1,2],[4,2],[4,5],[1,2]],"color":"#2563eb"}],"points":[{"x":1,"y":2,"label":"A"},{"x":4,"y":2,"label":"B"},{"x":4,"y":5,"label":"C"}]} ```
2Task 2
Triangle has vertices , , (same triangle as Task 1). This time, translate it using the rule . Write the new coordinates and plot both triangles. Then measure and compare one pair of corresponding side lengths on your board.

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