Pythagorean+theorem+proof+method

== = Pythagorean theorem : In a right triangle, the hypotenuse is equal to the square of side length squared of the two right angles , and Collage. If the triangle are two right angle sides a, b, hypotenuse is c, then a ^ 2; + b ^ 2; = c ^ 2;, that is, α * α + b * b = c * c Promotion : the index to n, the equality becomes less than the number = = As shown, this is the 20th President of the United States to prove the Pythagorean theorem when Garfield graphics used, with two congruent isosceles right triangle and a right angle to spell out a trapezoid -shaped three solutions. With this graph, you can use the Pythagorean theorem -area method to verify it? Test sites : the proof of the Pythagorean theorem. Topics: proofs. Analysis : The area of ​​the triangle and trapezoidal area to represent the graphics area, total and to prove the Pythagorean theorem. Answer : Solution : This diagram can be understood, there are three Rt △ the area were ab, ab, and c2. There is also a right-angled trapezoid, its area is (ab) (ab). We can see from the graph : (a b) (a b) = ab ab c2 Order was (a b) 2 = 2ab c2, a2 ​​b2 2ab = 2ab c2, ∴ a2 b2 = c2. Thus verify the Pythagorean theorem. Comments : The main problem area of ​​a triangle using the formula : base × height ÷ 2, and the trapezoid area formula : ( on the bottom end ) × height ÷ 2. = = = = Figure : Given two completelyequalright triangle,hypotenuselengtharec,at right angles tothe longersideofb,shortforc.Proof:extend theBEand ADintersect atpointE.Are : △ AEF ∽ △ ACD ∴ EF / CD = AF / AD = AE / AC = a / b∴ EF = a ^ 2 / b AF = ac / b ∵exactly equal totworight-angled triangle∴ ∠ BAE + ∠ FAE = 90 °∴In theright triangleBAF, there are: 1/2AE × BF = 1/2BA × AF (△ BAFarea ) ∴ AE × (BE + EF) = BA × AFNamely : a (b + a ^ 2 / b) = c (ac / b) Simplification , too : a ^ 2 + b ^ 2 = c ^ 2=