Standard #: MAFS.8.G.2.6 (Archived Standard)

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

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

Students are asked to explain the steps of a proof of the converse of the Pythagorean Theorem.

Students will complete a hands-on activity to discover a geometric proof of the Pythagorean Theorem, and they will use and apply the Pythagorean Theorem to solve examples and real-world situations.

Students will complete a hands-on activity to discover a geometric proof of the Pythagorean Theorem, and they will use and apply the Pythagorean Theorem to solve examples and real-world situations.

In this first of three lessons on the Pythagorean Theorem students work to prove the Pythagorean theorem and verify that the theorem works.

Students are guided through a short history of Pythagoras and a discovery of the Pythagorean Theorem using the squaring of the sides of a right triangle.

Students will complete a hands-on activity to discover a geometric proof of the Pythagorean Theorem, and they will use and apply the Pythagorean Theorem to solve examples and real-world situations.

In this first of three lessons on the Pythagorean Theorem students work to prove the Pythagorean theorem and verify that the theorem works.

Students are guided through a short history of Pythagoras and a discovery of the Pythagorean Theorem using the squaring of the sides of a right triangle.

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra and addresses the following national standards of the National Council of Teachers of Mathematics and the Mid-continent Research for Education and Learning: 1) Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; 2) Use visualization, spatial reasoning, and geometric modeling to solve problems; 3) Understand and apply basic and advanced properties of the concepts of geometry; and 4) Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems. The video portion is about thirty minutes, and with breaks could be completed in 50 minutes. (You may consider completing over two classes, particularly if you want to allow more time for activities or do some of the enrichment material). These activities could be done individually, in pairs, or groups. I think 2 or 3 students is optimal. The materials required for the activities include scissors, tape, string and markers.

This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.

This video demonstrates Bhaskara's proof of the Pythagorean Theorem.

This video shows a proof of the Pythagorean Theorem using similar triangles.

This resource gives an animated and then annotated proof of the Pythagorean Theorem.

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra and addresses the following national standards of the National Council of Teachers of Mathematics and the Mid-continent Research for Education and Learning: 1) Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; 2) Use visualization, spatial reasoning, and geometric modeling to solve problems; 3) Understand and apply basic and advanced properties of the concepts of geometry; and 4) Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems. The video portion is about thirty minutes, and with breaks could be completed in 50 minutes. (You may consider completing over two classes, particularly if you want to allow more time for activities or do some of the enrichment material). These activities could be done individually, in pairs, or groups. I think 2 or 3 students is optimal. The materials required for the activities include scissors, tape, string and markers.

This video demonstrates Bhaskara's proof of the Pythagorean Theorem.

This video shows a proof of the Pythagorean Theorem using similar triangles.

This resource gives an animated and then annotated proof of the Pythagorean Theorem.