Standard #: MAFS.912.G-SRT.2.4 (Archived Standard)

Students are asked to prove the Pythagorean Theorem using similar triangles.

Students are asked to prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.

Students are asked to prove that if a line intersecting two sides of a triangle divides those two sides proportionally, then that line is parallel to the third side.

Students are asked to prove that a line parallel to one side of a triangle divides the other two sides of the triangle proportionally.

Students will use Triangle Similarity to derive the proof of the Pythagorean Theorem and apply this method to develop the idea of the geometric mean with respect to the relationships in right triangles.

This lesson enriches the students' perspective of geometric proofs that are not in two-column form. Students will apply algebaic skills and geometric properties to prove the Pythagorean Theorem in a variety of ways. This unit is designed to help you identify and assist students who have difficulties in:

• Interpreting diagrams.
• Identifying mathematical knowledge relevant to an argument.
• Linking visual and algebraic representations.
• Producing and evaluating mathematical arguments.

This lesson unit is intended to help you assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables and develop experimental and analytical models of a physical situation.

Use properties, postulates, and theorems to prove a theorem about a triangle. In this interactive tutorial, you'll also learn how to prove that a line parallel to one side of a triangle divides the other two proportionally.

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.

Using a triangle with line through it, students are tasked to show the congruent angles, and conclude if one triangle is similar to the other.

In the eighth grade, your students were introduced to the Pythagorean Theorem and its converse. They applied this theorem to a variety of real-world and mathematical problems to find the lengths of sides of right triangles. Now that your students understand concepts related to similarity, they are able to appreciate a simple proof of the Pythagorean Theorem. The focus of this tutorial is on describing and explaining a proof of the Pythagorean Theorem using similar triangles.

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

This video visually proves the Pythagorean Theorem using triangles and parallelograms.

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.

Use properties, postulates, and theorems to prove a theorem about a triangle. In this interactive tutorial, you'll also learn how to prove that a line parallel to one side of a triangle divides the other two proportionally.

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.

Using a triangle with line through it, students are tasked to show the congruent angles, and conclude if one triangle is similar to the other.

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

This video visually proves the Pythagorean Theorem using triangles and parallelograms.

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.

Using a triangle with line through it, students are tasked to show the congruent angles, and conclude if one triangle is similar to the other.