The Pythagorean Theorem - Educational Outreach

3.4) Adding a DimensionInscribe a right triangle in cattycorner fashion andwithin a rectangular solid having the three side lengths A,B, and C as shown in Figure 3.4. Once done, thePythagorean Theorem can be easily extended to threedimensions as follows.DCXBAFigure 3.4: Three Dimensional Pythagorean TheoremExtension Theorem: Let three mutually-perpendicular linesegments have lengths A, B and C respectively, and letthese line segments be joined in unbroken end-to-endfashion as shown in Figure 3.4. Then the square of thestraight-line distance from the beginning of the firstsegment to the end of the last line segment is given byA2 B2 C2 D2Proof: From the Pythagorean Theorem, we haveX2 C2 Dtime, we haveXAA2222 C B B. From the Pythagorean Theorem a secondA2222 B D X C2222 X& D22. Thus98