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File:Pythagoras similar triangles simplified.svg

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English: Simplified version of similar triangles proof for Pythagoras' theorem.

In triangle ACB, angle ACB is the right angle. CH is a perpendicular on hypotenuse AB of triangle ACB.
In triangle AHC and triangle ACB, ∠AHC=∠ACB as each is a right angle. ∠HAC=∠CAB as they are common angles at vertex A. Thus triangle AHC is similar to triangle ACB by AA test.
Thus,    

In triangle BHC and triangle ACB, ∠BHC=∠ACB as each is a right angle. ∠HBC=∠CBA as they are common angles at vertex B. Thus triangle BHC is similar to triangle BCA by AA test.
Thus,    




which is the Pythagoras theorem.
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This file was derived from: Pythagoras similar triangles.svg
Reference:

[1]
  1. (2011) GEOMETRY Standard X, Secretary, Maharashtra State Board of Secondary and Higher Secondary Education, Pune-411 004, pp. 22, 23
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This W3C-unspecified vector image was created with Inkscape .


This is a retouched picture, which means that it has been digitally altered from its original version. Modifications: Simplified and removed lower-case notations and related elements per some comments at Wikipedia:Featured picture candidates/Pythagoras similar triangles proof. The original can be viewed here: Pythagoras similar triangles.svg. Modifications made by Gauravjuvekar.

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Public domain This image of simple geometry is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship.
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Original upload log

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This image is a derivative work of the following images:

  • File:Pythagoras_similar_triangles.svg licensed with PD-shape
    • 2012-04-10T12:17:44Z Gauravjuvekar 811x660 (10457 Bytes) validation
    • 2012-03-17T14:50:09Z Gauravjuvekar 811x660 (15195 Bytes) Reverted to version as of 14:18, 17 March 2012, arrows
    • 2012-03-17T14:32:05Z Gauravjuvekar 512x417 (8557 Bytes) Removing line-height attribute (11 times)
    • 2012-03-17T14:22:42Z Gauravjuvekar 512x417 (8647 Bytes) validation
    • 2012-03-17T14:18:52Z Gauravjuvekar 811x660 (15195 Bytes) == {{int:filedesc}} == {{Information |Description={{en|1=Similar triangles for Pythagoras' theorem}} |Source={{Derived from|Pythagoras_similar_triangles.PNG|display=50}} |Date=2012-03-17 14:16 (UTC) |Author=*[[:File:Pythagora

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Date/TimeThumbnailDimensionsUserComment
current10:15, 15 May 2012Thumbnail for version as of 10:15, 15 May 2012512 × 385 (2 KB)Gauravjuvekar (talk | contribs)== {{int:filedesc}} == {{Information |Description={{en|1=Simplified version of similar triangles proof for Pythagoras' theorem.<br /> In triangle ACB, angle ACB i...

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