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Mathematics · Grade 8

Transformations and Congruence

Learners study the three rigid motions (translations, reflections and rotations), verify that they keep lengths, angle measures and parallel lines, and describe them with coordinate rules, including reflections across the axes and 90° and 180° rotations about the origin. The course ends by defining congruence as a sequence of rigid motions and by finding and checking such sequences.

  • 4 lessons
  • About 90 minutes
  • Transformations and congruence check: 10 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, put in order and sort into groups
See plans Included with Family, Teacher and School plans. Open in PlayOwl

What learners will discover

  • Verify that translations, reflections and rotations keep lengths, angle measures and parallel lines, and identify what can change (position and facing).
  • Use coordinates to describe and carry out translations, (x, y) → (x + a, y + b), and reflections across the x-axis and the y-axis.
  • Use coordinates to describe and carry out rotations of 90° (clockwise and counterclockwise) and 180° about the origin.
  • Explain that two figures are congruent when a sequence of rigid motions maps one onto the other, and describe and check such a sequence.

Lessons

  1. Rigid motions and what they keep 8 steps5 practiceabout 20 min
  2. Translations and reflections with coordinates 9 steps5 practiceabout 23 min
  3. Rotations about the origin 9 steps6 practiceabout 23 min
  4. Congruence as a sequence of rigid motions 9 steps6 practiceabout 24 min
  5. Transformations and congruence check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Algebra BalanceKeep the scale level and the equation true, step by step.
  • Function FactoryFeed the machine, crack its rule and predict what comes out.

More 8th grade math

Guide for grown-ups