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Mathematics · Grade 8

Similarity and Angle Relationships

Learners describe dilations with coordinates and scale factors, define similarity as rigid motions plus dilations, and use scale factors to find missing lengths. They then find angles formed when parallel lines are cut by a transversal, explain why a triangle's angles add to 180° and why an exterior angle equals the sum of the two remote interior angles, and use the angle-angle criterion to prove triangles similar and solve measurement problems.

  • 4 lessons
  • About 95 minutes
  • Similarity and angles check: 10 questions
  • Ways to answer: choose an answer, type a fraction, plot points, match pairs, type a number and put in order
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What learners will discover

  • Use coordinates to describe dilations centered at the origin, (x, y) → (kx, ky), and find and interpret scale factors.
  • Explain that two figures are similar when a sequence of rigid motions and dilations maps one onto the other, and use the scale factor to find missing lengths.
  • Find unknown angles formed when parallel lines are cut by a transversal, including by writing and solving equations.
  • Explain the triangle angle sum and exterior angle facts, and use the angle-angle criterion to show triangles are similar and to find unknown lengths.

Lessons

  1. Dilations on the coordinate plane 9 steps5 practiceabout 23 min
  2. Similar figures and missing lengths 9 steps5 practiceabout 24 min
  3. Parallel lines cut by a transversal 9 steps5 practiceabout 24 min
  4. Triangle angles and AA similarity 9 steps6 practiceabout 24 min
  5. Similarity and angles 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