G.2.6

Explain a proof of the Pythagorean Theorem and its converse.

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Formative Assessments
Formative Assessments
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CPALMS: Students are asked to explain the steps of a proof of the converse of the Pythagorean Theorem.

Converse of the Pythagorean Theorem

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CPALMS: Students are asked to explain the steps of a proof of the Pythagorean Theorem that uses similar triangles.

Explaining a Proof of the Pythagorean Theorem

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CPALMS: Students are asked to explain how a pair of figures demonstrates the Pythagorean Theorem and its converse.

Pythagorean Squares

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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CPALMS: This resource is a representation to illustrate the Pythagorean Theorem.

Demonstrate the Pythagorean Theorem

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CPALMS: This resource, from NLVM will help teachers and students validate the Pythagorean Theorem both geometrically and algebraically. It can be used interactively to better understand the topic.

Pythagorean Theorem Manipulatives

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Assessment Questions
Assessment Questions
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Open Response
Videos of Expert Instruction
Videos of Expert Instruction
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This resource gives an animated and then annotated proof of the Pythagorean Theorem.
Annotated Proof of the Pythagorean Theorem
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In this fun video (approx. 12:50 min), Rob explains the importance of prior understandings before using detailed examples to show and explain how to use the Pythagorean Theorem to find the length of an unknown side of a triangle as well as to prove if a triangle is a right triangle.
“Pythagorean Theorem” by Math Antics
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This video (approx. 3:50 min.) demonstrates how to prove the Pythagorean Theorem using the area of a square and its components.
Pythagorean Theorem by LearnZillion
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In this video lesson (approx. 4:30 min.) a right triangle's legs and hypotenuse are shown to explain the Pythagorean Theorem, as well as displaying a model in order to explain its converse.

“Using the Pythagorean Theorem” by cK-12

Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: This task provides a chance both to emphasize the difference between the Pythagorean Theorem and its converse (which is less well known), while also providing an opportunity for experimentation.

Converse of the Pythagorean Theorem

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This lesson, using a video clip from ``The Wizard of Oz``, can be used as a hook to engage students with interest in exploring the Pythagorean Theorem in order to see exactly what the Scarecrow says regarding the sides of triangles that is not exactly mathematically correct.

“How Can We Correct the Scarecrow?” by Robert Kaplinsky