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Mathematics · Grade 10

Similarity and Scale

Learners study dilations and their properties, define similarity with similarity transformations, and use the AA, SAS and SSS similarity criteria to find unknown lengths, including indirect measurement with shadows. They prove the triangle proportionality (side-splitter) theorem and the Pythagorean theorem with similar triangles, and apply scale factors to maps, models, areas and volumes. An optional honors lesson develops geometric means in right triangles.

  • 5 lessons
  • About 135 minutes
  • Similarity and scale check: 11 questions
  • Ways to answer: choose an answer, plot points, type a number, put in order, sort into groups and true or false
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What learners will discover

  • Perform dilations with a given center and scale factor and use their properties: lengths scale by the factor, angles are preserved, and lines map to parallel lines.
  • Decide whether triangles are similar using similarity transformations or the AA, SAS and SSS similarity criteria, and find missing lengths with proportions.
  • Prove and apply the Triangle Proportionality Theorem and its converse, and explain a similarity proof of the Pythagorean theorem.
  • Solve scale-drawing and map problems and apply the effect of a scale factor k on perimeter (k), area (k^2^) and volume (k^3^).

Lessons

  1. Dilations 6 steps4 practiceabout 28 min
  2. Similar triangles 5 steps3 practiceabout 30 min
  3. The side-splitter theorem and similarity proofs 6 steps4 practiceabout 32 min
  4. Scale, area and volume 7 steps5 practiceabout 30 min
  5. Going further (honors): geometric means in right triangles 4 steps1 practiceabout 15 min
  6. Similarity and scale check 11 questions at the end

Keep exploring

More 10th grade math

Guide for grown-ups