8.3 - Squares and the Pythagorean Theorem

 Introduction:

This is a set of guiding questions and materials for creating your own lesson plan on the Pythagorean Theorem.

 

 Common Core State Standards:

  • 8.G.6
  • G-CO.1

 

 Learning Objectives:

  • To understand the relationship between rectangles and squares based on their definitions.
  • To explore nested definitions, as we did with relations and functions.
  • To intuitively understand the triangle inequality.
  • To understand one proof of the Pythagorean Theorem.

 

 Guiding Questions:

  • What can you say about the following two statements?
    • Every square is a rectangle, but not every rectangle is a square.
    • Every rectangle is a square, but not every square is a rectangle.
  • What is a square? What is a rectangle?
  • Can you create nested definitions showing the connections between polygons, quadrilaterals, parallelograms, rectangles, and squares?
    • Watch video.
  • The squares below are made of gold, where the square pans have the same depth and the white triangular space is a right triangle. If you are given a choice between the large yellow square and the two smaller green squares, what would you choose?

8.3_diagram1.png

  • What do you need to solve this problem?
  • How can you compute and compare the areas of the squares to be certain of your choice?

 

 Notes for Teachers:

  • I have indented some suggestions in the questions above.
  • At this stage, most students have already been introduced to the Pythagorean Theorem, so we want to build on that and solidify that knowledge.
  • Watch the video of one proof of the Pythagorean Theorem.

 

 Video of the Day:

8.3.1 Sum of Interior Angles of a Triangle

We prove that the sum of the interior angles of a triangle is 180o.

 8.3.1 Sum of Angles in Triangles.mp4 Download 8.3.1 Sum of Angles in Triangles.mp4Play media comment.

 

8.3.2 The Pythagorean Thoerem

We show what we consider to be one of the simplest proofs of this famous result, which resembles Bhaskara’s proof.

8.3.2 The Pythagorean Theorem.mp4 Download 8.3.2 The Pythagorean Theorem.mp4Play media comment.

 

 Exercises and Problems:


 

 Additional Resource for Teachers:

If you wish to download the contents of this page as a printable pdf, click here:  Download 8.3 Squares and the Pythagorean Theorem.pdf