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Geometry of a Tetrahedron: Question 3: 3D Pythagorean Theorem

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First published at 17:04 UTC on March 16th, 2023.

#mathematics
#science
#geometry

Math Easy Solutions

MES

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In this video I go over Question 3 of the Discovery Project: Geometry of a Tetrahedron. This question uses the results from Question 1, in which I calculated the areas of the 4 triangular faces. Using those results, I show that the area squared of the opposite triangular face is equal to the sum of the squares of the 3 areas adjacent to the opposite vertex. In other words, we have a three-dimensional version of the Pythagorean Theorem: D^2 = A^2 + B^2 + C^2

This video was taken from my earlier video listed below:

- Discovery Project: The Geometry of a Tetrahedron: https://youtu.be/yRws7Jk2iHU
- Video notes: https://peakd.com/hive-128780/@mes/discovery-project-geometry-of-a-tetrahedron
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GoEi9wxl8nTFcfw1ay-_1T .

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