NASA: Pythagorean Theorem

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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.

https://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html

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

Intended Users	Formats	Ratings
- Learners - Educators - General Publics	- application/java - text/html	Currently 0.0/5 Want to rate this material? Login here!

Access Rights:: Free access
Restriction:: Does not have a copyright, license, or other use restriction.
Courtesy of:: NASA Glenn Research Center
Keywords:: 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
Other Collections:: The Physics Front

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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.

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Record Link

<a href="https://www.compadre.org/portal/items/detail.cfm?ID=8390">NASA Glenn Learning Technologies Project. NASA: Pythagorean Theorem. Cleveland: NASA Glenn Learning Technologies Project, January 27, 2008.</a>

AIP Format

(NASA Glenn Learning Technologies Project, Cleveland, 2004), WWW Document, (https://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html).

AJP/PRST-PER

NASA: Pythagorean Theorem (NASA Glenn Learning Technologies Project, Cleveland, 2004), <https://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html>.

APA Format

NASA: Pythagorean Theorem. (2008, January 27). Retrieved May 2, 2025, from NASA Glenn Learning Technologies Project: https://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. https://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html (accessed 2 May 2025).

MLA Format

NASA: Pythagorean Theorem. Cleveland: NASA Glenn Learning Technologies Project, 2004. 27 Jan. 2008. 2 May 2025 <https://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 = {2025}, Number = {2 May 2025}, 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 https://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 2025 %N 2 May 2025 %8 January 27, 2008 %9 application/java %U https://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.

The Chicago Style presented is based on information from Examples of Chicago-Style Documentation.

The MLA Style presented is based on information from the MLA FAQ.

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