Lesson Plan


Students use the Pythagorean theorem to solve a tricky puzzle involving a square with four isosceles triangles cut from the corners.


  • Mathematics > General
  • Mathematics > Geometry
  • Mathematics > Problem Solving

Education Levels:

  • Grade 6
  • Grade 7
  • Grade 8
  • Grade 9
  • Grade 10
  • Grade 11
  • Grade 12


geometry measurement coordinate conjecture pythagorean theorum triangle triangles



Access Privileges:

Public - Available to anyone

License Deed:

Creative Commons Attribution 3.0


Update Standards?

CCSS.Math.Content.HSF-TF.C.8: Common Core State Standards for Mathematics

Prove the Pythagorean identity sin²(?) + cos²(?) = 1 and use it to find sin(?), cos(?), or tan(?) given sin(?), cos(?), or tan(?) and the quadrant of the angle.

CCSS.Math.Content.HSG-SRT.B.4: Common Core State Standards for Mathematics

Prove theorems about triangles.

CCSS.Math.Content.HSG-SRT.C.8: Common Core State Standards for Mathematics

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.?

S2487000: Texas Essential Knowledge and Skills for Mathematics

use models and diagrams to explain the Pythagorean theorem.
Curriki Rating
On a scale of 0 to 3
On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2009-07-26.

Component Ratings:

Technical Completeness: 3
Content Accuracy: 3
Appropriate Pedagogy: 2

Reviewer Comments:

An interesting problem with an interesting solution. This problem has a wrinkle that the author left out: when you declare that the sum of the four triangle is fixed (ie 200), you require that the original square grow or shrink depending on where you cut the side. This becomes obvious if you try the 2 extreme cases: cut the square at the end or in the middle.

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