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.

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.

NASA: Pythagorean Theorem. (2008, January 27). Retrieved May 28, 2015, from NASA Glenn Learning Technologies Project: http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html

%0 Electronic Source %D January 27, 2008 %T NASA: Pythagorean Theorem %I NASA Glenn Learning Technologies Project %V 2015 %N 28 May 2015 %8 January 27, 2008 %9 application/java %U http://www.grc.nasa.gov/WWW/K-12/airplane/pythag.html

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