Provides examples and a video lesson that illustrate the Pythagorean Theorem which provides us with the relationship between the sides in a right triangle. [4:41]

This interactive exercise focuses on using the Pythagorean Theorem to calculate distance and plotting points on a Cartesian grid.

This video lesson demonstrates how to calculate the area of a triangle. It includes detailed examples including ones that use the Pythagorean Theorem. Students can check their understanding with an assessment. [10:43]

Students learn the importance of the Pythagorean theorem as applied in radar imaging. They use a sensor unit with IRED (infrared emitting diode) to measure triangle distances and the theorem to calculate and verify distances. Student groups calibrate the sensor units to ensure accurate distance measurements. A "pretend" outdoor radar imaging model is provided to groups for sensor unit testing.

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.

The focus of the lesson is to review and strengthen understanding of the Pythagorean Thm and the Converse of the Pythagorean Thm.  In addition review and strengthen the students algebra skills regarding square roots.This cover Ohio Standards in geometry:Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. 

This lesson will demonstrate how to use the converse of the Pythagorean Theorem to determine if three side lengths of a triangle form a right triangle. It is 5 of 5 in the series titled "Converse of the Pythagorean Theorem." [8:28]

The x and y coordinates of the unit circle are discussed here, in the context of right triangles.

This site from Cut The Knot provides an overview of the law of cosines, complete with an explanation of the law and a proof of the law.

Students use simple materials to design an open spectrograph so they can calculate the angle light is bent when it passes through a holographic diffraction grating. A holographic diffraction grating acts like a prism, showing the visual components of light. After finding the desired angles, students use what they have learned to design their own spectrograph enclosure.

This lesson focuses on exponents and radicals as they apply to problems involving squares, perfect squares, and square roots.

At the end of this lesson plan about formulas, students will be able to identify and apply the correct formula for a given situation, solve for any unknown component of the formulas for perimeter, circumference, and area of regular and irregular shapes, and volume, and use the Pythagorean Theorem in the context of real-life situations.

Explains the basic concept of the Pythagorean Theorem with step-by-step instructions and methods for solving specific problems on your own relating to this topic.

Explains the basic concept of right triangles with step-by-step instructions and methods for solving specific problems on your own relating to this topic.

This stand-alone module examines the history, applications, and various proofs of the Pythagorean Theorem. The module also includes student activities and exercise problems. The module assumes the reader has a basic geometry background.

In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.  The module begins with the definition of dilation, properties of dilations, and compositions of dilations.  One overarching goal of this module is to replace the common idea of “same shape, different sizes” with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Module 7 begins with work related to the Pythagorean Theorem and right triangles.  Before the lessons of this module are presented to students, it is important that the lessons in Modules 2 and 3 related to the Pythagorean Theorem are taught (M2:  Lessons 15 and 16, M3:  Lessons 13 and 14).  In Modules 2 and 3, students used the Pythagorean Theorem to determine the unknown length of a right triangle.  In cases where the side length was an integer, students computed the length.  When the side length was not an integer, students left the answer in the form of x2=c, where c was not a perfect square number.  Those solutions are revisited and are the motivation for learning about square roots and irrational numbers in general.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Students explore the concept of similar right triangles and how they apply to trigonometric ratios. Use this lesson as a refresher of what trig ratios are and how they work. In addition to trigonometry, students explore a clinometer app on an Android® or iOS® device and how it can be used to test the mathematics underpinning trigonometry. This prepares student for the associated activity, during which groups each put a clinometer through its paces to better understand trigonometry.