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published by the NASA Glenn Learning Technologies Project
This resource features an animated Java tutorial that uses geometric overlays to show why the Pythagorean Theorem works. The resource was developed by NASA to supplement the algebraic proofs which are typically provided to students for solving problems involving right triangles.  Background information on the Pythagorean Theorem and its historical use is included.  

This resource is part of a larger collection, developed by scientists and teacher workshop participants at NASA's Glenn Learning Research Center.

Please note that this resource requires Java Applet Plug-in.
Editor's Note: Many students can benefit greatly by visualizing why a formula works. This applet is simple enough for middle school, yet very effectively shows the spatial relationships that exist among the right triangle and the squares of its three sides.
Subjects Levels Resource Types
Classical Mechanics
- Motion in Two Dimensions
= Position & Displacement
Other Sciences
- Mathematics
- High School
- Middle School
- Informal Education
- Instructional Material
= Simulation
= Tutorial
Appropriate Courses Categories Ratings
- Physical Science
- Physics First
- Conceptual Physics
- Algebra-based Physics
- Activity
- New teachers
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Intended Users:
General Public
Access Rights:
Free access
Does not have a copyright, license, or other use restriction.
Courtesy of:
NASA Glenn Research Center
simulation, trigonometry, tutorial, vectors
Record Cloner:
Metadata instance created December 22, 2008 by Caroline Hall
Record Updated:
February 6, 2013 by Caroline Hall
Last Update
when Cataloged:
January 27, 2008

AAAS Benchmark Alignments (2008 Version)

2. The Nature of Mathematics

2A. Patterns and Relationships
  • 9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.

9. The Mathematical World

9B. Symbolic Relationships
  • 9-12: 9B/H5. When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes by more than one, and sometimes not at all.
9C. Shapes
  • 6-8: 9C/M9. Relationships exist among the angles between the sides of triangle and the lengths of those sides. For example, when two sides of a triangle are perpendicular, the sum of the squares of the lengths of those sides is equal to the square of the third side of the triangle.
  • 6-8: 9C/M10. Geometric relationships can be described using symbolic equations.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

Geometry (K-8)

Understand and apply the Pythagorean Theorem. (8)
  • 8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

High School — Geometry (9-12)

Similarity, Right Triangles, and Trigonometry (9-12)
  • G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Craft and Structure (6-12)
  • RST.9-10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9—10 texts and topics.
Integration of Knowledge and Ideas (6-12)
  • RST.6-8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).
Range of Reading and Level of Text Complexity (6-12)
  • RST.6-8.10 By the end of grade 8, read and comprehend science/technical texts in the grades 6—8 text complexity band independently and proficiently.

This resource is part of a Physics Front Topical Unit.

Topic: Kinematics: The Physics of Motion
Unit Title: Vectors

This simple, yet effective Java-based tutorial uses geometric overlays to demonstrate why the Pythagorean Theorem works.  Background text helps students understand its importance in vector algebra.

Link to Unit:
ComPADRE is beta testing Citation Styles!

Record Link
AIP Format
(NASA Glenn Learning Technologies Project, Cleveland, 2004), WWW Document, (http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html).
NASA: Pythagorean Theorem, (NASA Glenn Learning Technologies Project, Cleveland, 2004), <http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html>.
APA Format
NASA: Pythagorean Theorem. (2008, January 27). Retrieved December 16, 2017, from NASA Glenn Learning Technologies Project: http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html
Chicago Format
NASA Glenn Learning Technologies Project. NASA: Pythagorean Theorem. Cleveland: NASA Glenn Learning Technologies Project, January 27, 2008. http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html (accessed 16 December 2017).
MLA Format
NASA: Pythagorean Theorem. Cleveland: NASA Glenn Learning Technologies Project, 2004. 27 Jan. 2008. 16 Dec. 2017 <http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html>.
BibTeX Export Format
@misc{ Title = {NASA: Pythagorean Theorem}, Publisher = {NASA Glenn Learning Technologies Project}, Volume = {2017}, Number = {16 December 2017}, Month = {January 27, 2008}, Year = {2004} }
Refer Export Format

%T NASA: Pythagorean Theorem
%D January 27, 2008
%I NASA Glenn Learning Technologies Project
%C Cleveland
%U http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html
%O application/java

EndNote Export Format

%0 Electronic Source
%D January 27, 2008
%T NASA: Pythagorean Theorem
%I NASA Glenn Learning Technologies Project
%V 2017
%N 16 December 2017
%8 January 27, 2008
%9 application/java
%U http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html

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Citation Source Information

The AIP Style presented is based on information from the AIP Style Manual.

The APA Style presented is based on information from APA Style.org: Electronic References.

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Is Part Of NASA: Beginner's Guide to Aerodynamics - Aerodynamics Index

This is the full collection on the topic of aerodynamics, developed by the NASA Glenn Learning Research Center.

relation by Caroline Hall

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