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Form 2 Mathematics
Visual proof of Pythagoras' Theorem
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Preliminary knowledge Drag the points A and C to shear the quadrilateral ABCD. What can you about the area of ABCD? Does shearing affect the area? |
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The Visual Proof 1. Drag the point P, and then the point Q, to shear the squares on the legs. Shearing does not affect a polygon's area. 2. Drag the point R to shear the square to fill the right angle. Note that the resulting shapes are congruent. Press "r" to reset the sketch.Click here to download the Word document showing the idea of the deductive proof. |
Definitions:
The side opposite the right angle in a right triangle is called the hypotenuse. (This term applies only to right triangles.) The two other sides (those forming the right angle) are called legs. Often the legs are labeled a and b and the hypotenuse is labeled c. Usually the angles opposite the sides of a triangle have the same letters, but capitalized: A, B, and C.
The Pythagoras' Theorem:
(a) In a right triangle with legs a and b and hypotenuse c, a2+b2
= c2
(b) If a triangle has sides a, b, and c, and a2+b2
= c2 then the triangle is a right triangle with hypotenuse
c.
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Puzzle Can you cut the five shaded pieces in the largest square and paste to the other two smaller squares? Press "r" to reset the sketch. |
A related web site in Japan with various "visual" proofs of Pythagoras' Theorem.
A Java sketch created by a 12-year-old student in Brazil showing a puzzle about Pythagoras' Theorem
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