![]() ![]() With these methods, we can not only prove difficult geometric theorems but also discover new theorems and generate short and readable proofs. The four identical red triangles create a square in the activity below, combined with a square that is the size of the hypotenuse of the triangle. In algebraic terms, a2 + b2 c2 where c is the hypotenuse while a and b are the sides of the triangle. Pythagoras' Theorem then claims that the sum of (the areas of) two small squares equals (the area of) the large one. As a theorem prover, MMP/Geometer implements Wu’s method for Euclidean and differential geometries, the area method and the geometric deductive database method. The third and final proof of the Pythagorean Theorem that we’re going to discuss is the proof that starts off with a right angle. Pythagorean Theorem and its many proofs Pythagorean Theorem Let's build up squares on the sides of a right triangle. We introduce a software package, MMP/Geometer, developed by us to automate some of the basic geometric activities including geometric theorem proving, geometric theorem discovering, and geometric diagram generation. Young geometers use technology (Geometers Sketchpad) to explore the Pythagorean Theorem and analyze different proofs. Dividing each term on both sides by c 2, a 2 / c 2 + b 2 / c 2 c 2 / c 2 (a / c) 2 + (b / c) 2 1 (cos ) 2 + (sin ) 2 1 (or) sin 2 + cos 2 1. The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared. Applying the Pythagoras theorem to the triangle, we get. Proof of Pythagorean Identity sin + cos 1. ![]() MMP/Geometer – a software package for automated geometric reasoning. Let us prove each pythagorean trig identity one by one.
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