The Pythagorean Theorem - Educational Outreach

If a parallelogram of area A3is fitted to side AB via theconstruction method in Figure 3.10, then A1 A2 A3.DdCA1A2AdEA 3BFA1 A2 A3Figure 3.10: Diagram for Pappus’ TheoremProof of Pappus’ Theorem:1 : Let ABC be a general triangle. Fit an arbitraryparallelogram of area A1to the side AC ; likewise, fit thearbitrary parallelogram of area A2to the side BC .2 : Linearly extend the outer sides—dotted lines—of thetwo fitted parallelograms until they meet at the point D.3 : Construct a dashed shear line through the points Dand C as shown in Figure 3.10. Let DC EF d .Construct two additional shear lines through points A andB with both lines parallel to the line passing through pointsD and C.108