File:Pythagoras by similar triangles.PNG
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Pythagoras_by_similar_triangles.PNG (583 × 562 pixels, file size: 21 KB, MIME type: image/png)
Summary
A similarity proof for Pythagoras' theorem based upon areas proportional to sides on the center triangle. Area of triangle C = sum of areas of A and B. All three right triangles are similar, so all three areas are proportional to the side bordering the center triangle. Hence, α(a2 + b2) = α c2, or dividing by α, we have Pythagoras' theorem.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 14:11, 9 January 2017 | 583 × 562 (21 KB) | 127.0.0.1 (talk) | A similarity proof for Pythagoras' theorem based upon areas proportional to sides on the center triangle. Area of triangle C = sum of areas of A and B. All three right triangles are similar, so all three areas are proportional to the side bordering the center triangle. Hence, α(a<sup>2</sup> + b<sup>2</sup>) = α c<sup>2</sup>, or dividing by α, we have Pythagoras' theorem. |
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