Big Idea:

Big Idea 1

Corresponding sides of similar triangles prove the Pythagorean Theorem is true for all right triangles.

1 week

Evidence of Understanding

  • use triangle similarity and scale factor to prove relationships for right triangles
    • prove the Pythagorean Theorem (proof of the Pythagorean theorem using similarity)
    • use similarity to analyze relationships between the altitude and the lengths of the two segments of the hypotenuse
      • prove the length of the altitude drawn from the vertex of the right angle is the geometric mean between the lengths of the two segments of the hypotenuse (video)
      • calculate the length of an altitude or one of the two segments of the hypotenuse
         
  • analyze characteristics of triangles using the Pythagorean Theorem
    • classify a triangle as acute, right, or obtuse using the Pythagorean theorem
      • use an area model to explain that when a2 + b2 > c2, the triangle is acute; that when a2 + b2  = c2, the triangle is right; and that when a2 + b< c2, the triangle is obtuse
    • analyze and describe special Pythagorean triples using similarity and scale factor
      • explain that special triples occur when a2 + b2 is a perfect square and use this to strategically name Pythagorean triples
      • use similarity to explain and name other triangles that are similar to the 3-4-5, 5-12-13, 8-15-17, or other Pythagorean triples
         
  • find the missing side length of a right triangle using Pythagorean Theorem
    • create diagrams to model situations and use Pythagorean Theorem to solve them
      • use right triangles and their properties to describe objects and/or situations
      • use properties of similar triangles and scale factor with the Pythagorean Theorem
    • use a Pythagorean triple, when applicable, to state missing side lengths

Develop conceptual understanding:

Pythagorean Theorem, geometric mean, acute triangle, obtuse triangle, right triangle, perfect square, Pythagorean triple

Supporting terms to communicate:

perpendicular, altitude, vertex, corresponding, leg, hypotenuse, right angle, acute angle, obtuse angle, similar, scale factor, proportional, ratio
Core Resource
A core resource supports multiple days of instruction.
  • Proving the Pythagorean Theorem
    Resource:
    Proving the Pythagorean Theorem

    During this Core Resource, students explore the Pythagorean theorem and how similar triangles can be used in a variety of different ways to prove theorems about right triangles, including the Pythagorean theorem itself.

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