Illustrative Mathematics
Shortest Line Segment from a Point P to a Line L
One of the hardest skills for many young geometers to grasp is to move beyond just declaring obvious things true, and really returning to fundamental principles for proof. This brief exercise stretches those proving muscles as the...
Mathematics Vision Project
Module 6: Congruence, Construction, and Proof
Trace the links between a variety of math concepts in this far-reaching unit. Ideas that seem very different on the outset (like the distance formula and rigid transformations) come together in very natural and logical ways. This...
Mathematics Vision Project
Connecting Algebra and Geometry
Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates...
EngageNY
End-of-Module Assessment Task: Grade 8 Mathematics (Module 7)
It's time to discover what your classes have learned! The final lesson in the 25-part module is an assessment that covers the Pythagorean Theorem. Application of the theorem includes distance between points, the volume of...
Curated OER
Pythagorean Theorem
In this finding the missing units in triangles activity, students apply the Pythagorean Theorem to solve. Students solve 10 problems.
Curated OER
The Pythagorean Theorem
Students create both a visual and formal proof of the Pythagorean theorem, as well as view four additional geometric demonstrations of the theorem. They construct a square and conjecture the following theorem: The sum of the areas of...
EngageNY
Law of Cosines
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
University of Utah
Geometry: Angles, Triangles, and Distance
The Pythagorean Theorem is a staple of middle school geometry. Scholars first investigate angle relationships, both in triangles and in parallel lines with a transversal, before proving and applying the Pythagorean Theorem.
Shodor Education Foundation
Squaring the Triangle
Teach budding mathematicians how to square a triangle with an interactive that shows a graphical proof of the Pythagorean Theorem. Pupils alter the lengths of the legs using sliders. Using the inputted lengths, the applet displays the...
Mathematics Vision Project
Similarity and Right Triangle Trigonometry
Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...
Curated OER
Pythagorean Theorem Triples
Students research the concept of the Pythagorean Theorem. In this Pythagorean Theorem lesson, students use the Internet to learn about the Pythagorean Theorem. Students construct proofs of the Pythagorean Theorem.
Curated OER
Pythagorean Theorem
Students investigate the Pythagorean Theorem. In this seventh through twelfth grade geometery lesson, students explore the Pythagorean Theorem and its converse and use it to find the length of the missing side of a right...
Curated OER
Pythagoras' Theorem
Students are introduced to the Pythagoras' Theorem and its history, proofs and practice in application. Students find perimeters, areas and volume of everyday objects. Students state and explain the theory.
Curated OER
Central Valley Math Project
Middle schoolers study the Pythagorean Theorem. They describe what it means to square a number. Pupilsuse the Pythagorean Theorem to prove the sides of given triangles, and use geometric pieces of paper to create a right triangle and...
Curated OER
The Right Stuff
Studentsare introduced to the Pythagorean Theorem by exploring right triangles and the squares built on each side. They apply the Pythagorean Theorem to real-world problems. Students u se informal and nonformal arguments of proof (i.e.,...
EngageNY
Law of Sines
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
Curated OER
Discovering Math: Concepts in Geometry
Middle and high schoolers explore the concept of proving the Pythagorean Theorem. They research proofs of the Pythagorean Theorem. Pupils create posters of proofs, and research Greek mathematicians.
EngageNY
Graphing Systems of Equations
Expand on learners' understanding of quadratic-linear systems. Building on the graphic understanding developed in the previous lesson, pupils learn algebraic methods of solving the systems.
Curated OER
The Pythagorean Theorem
Seventh graders relate the Pythagorean theorem to the real world. For this algebra lesson, 7th graders identify important properties of the Pythagorean theorem and use it to solve word problems. They create a step by step plan to...
Curated OER
Picking Pythagoras
Students discover that side measurement is used in determining angle classification of a triangle. By squaring sides, they predict whether triangles be right, obtuse, or acute. They prove the Pythagorean Theorem and use it to solve...
EngageNY
Criterion for Perpendicularity
The Pythagorean Theorem is a geometry pupil's best friend! Learners explain the equation a1b1 + a2b2 = 0 for perpendicular segments using the Pythagorean Theorem. They are able to identify perpendicular segments using their...
Curated OER
Flying with Pythagoras
A lengthy narrative about Pythagoras and his students precedes an activity in which your young mathematicians practice using the Pythagorean theorem to solve three problems about flight and distance. Answers are provided.
Charleston School District
Review Unit 8: Geometry Applicaitons
Pupils complete a review activity that highlights the key problems from the first eight lessons in the series. Topics include the Pythagorean Theorem and its converse, as well as finding volume of three-dimensional figures.
Virginia Department of Education
Circles in the Coordinate Plane
Make the connection between the distance formula and the equation of a circle. The teacher presents a lesson on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the coordinate plane and...