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Mathematics · Grade 10

Triangle Properties and Proof

Learners prove the triangle angle-sum and exterior angle theorems, the isosceles triangle theorem and its converse, and use the triangle inequality and the midsegment theorem. They then meet the four classical points of concurrency (circumcenter, incenter, centroid and orthocenter), prove why the circumcenter is equidistant from the vertices, and apply the centroid's 2 : 1 property.

  • 4 lessons
  • About 125 minutes
  • Triangle properties check: 11 questions
  • Ways to answer: choose an answer, plot points, match pairs, type a number, place on a number line and put in order
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What learners will discover

  • Prove and apply the Triangle Angle-Sum Theorem and the Exterior Angle Theorem.
  • Prove and apply the Isosceles Triangle Theorem and its converse.
  • Apply the Triangle Inequality Theorem, the relationship between side lengths and opposite angles, and the Midsegment Theorem.
  • Identify and use the circumcenter, incenter, centroid and orthocenter, including the equidistance properties and the centroid's 2 : 1 ratio.

Lessons

  1. Angle sums and exterior angles 7 steps5 practiceabout 30 min
  2. Isosceles triangles 7 steps4 practiceabout 30 min
  3. The triangle inequality and midsegments 6 steps4 practiceabout 30 min
  4. Points of concurrency 7 steps5 practiceabout 32 min
  5. Triangle properties check 11 questions at the end

Keep exploring

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Guide for grown-ups