File:Pythagoras similar triangles.svg

Original file (SVG file, nominally 811 × 660 pixels, file size: 10 KB)

This is a file from the Wikimedia Commons. Information from its description page there is shown below.
Commons is a freely licensed media file repository. You can help.

Summary

Description

English: 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, ${\frac {AC}{AB}}={\frac {AH}{AC}}$ $\therefore {AC}^{2}={AB}\times {AH}$

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, ${\frac {BC}{AB}}={\frac {BH}{BC}}$ $\therefore {BC}^{2}={AB}\times {BH}$

$\therefore {AC}^{2}+{BC}^{2}=({AB}\times {AH})+({AB}\times {BH})$

$\therefore {AC}^{2}+{BC}^{2}={AB}\times ({AH}+{BH})$

$\therefore {AC}^{2}+{BC}^{2}={AB}\times {AB}$

\therefore {AC}^{2}+{BC}^{2}={AB}^{2}

which is the Pythagoras theorem.

Date

17 March 2012, 14:16 (UTC)

Source

This file was derived from: Pythagoras similar triangles.PNG:
Reference:

^[1]

↑ (2011) GEOMETRY Standard X, Secretary, Maharashtra State Board of Secondary and Higher Secondary Education, Pune-411 004, pp. 22, 23

Author

Pythagoras_similar_triangles.PNG: Brews ohare
derivative work: Gauravjuvekar

Other versions

A raster version of this image is available. It should be used in place of this vector image when superior.

File:Pythagoras similar triangles.svg → File:Pythagoras similar triangles.PNG

In general, it is better to use a good SVG version.

العربية ∙ Boarisch ∙ বাংলা ∙ čeština ∙ Deutsch ∙ English ∙ Esperanto ∙ español ∙ فارسی ∙ suomi ∙ français ∙ galego ∙ עברית ∙ hrvatski ∙ Bahasa Indonesia ∙ italiano ∙ 日本語 ∙ 한국어 ∙ македонски ∙ മലയാളം ∙ Plattdüütsch ∙ Nederlands ∙ polski ∙ português ∙ русский ∙ sicilianu ∙ slovenščina ∙ svenska ∙ Türkçe ∙ українська ∙ Tiếng Việt ∙ 中文（简体） ∙ 中文（繁體） ∙ +/−

English: A simplified version with lower-case notations(and related elements) removed

W3C-validity not checked.

This W3C-unspecified vector image was created with Inkscape .

This SVG file contains embedded text that can be translated into your language, using any capable SVG editor, text editor or the SVG Translate tool. For more information see: About translating SVG files.

Licensing

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.

Heptagon

Assessment

Quality image

This image has been assessed using the Quality image guidelines and is considered a Quality image.

العربية ∙ جازايرية ∙ беларуская ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ čeština ∙ Cymraeg ∙ Deutsch ∙ Schweizer Hochdeutsch ∙ Zazaki ∙ Ελληνικά ∙ English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ galego ∙ עברית ∙ हिन्दी ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ italiano ∙ 日本語 ∙ Jawa ∙ ქართული ∙ кыргызча ∙ 한국어 ∙ kurdî ∙ Lëtzebuergesch ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ मराठी ∙ Bahasa Melayu ∙ Nederlands ∙ Norfuk / Pitkern ∙ polski ∙ português ∙ português do Brasil ∙ qaraqalpaqsha ∙ rumantsch ∙ română ∙ русский ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ shqip ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ తెలుగు ∙ ไทย ∙ Tagalog ∙ toki pona ∙ Türkçe ∙ українська ∙ Oʻzbekcha ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（简体） ∙ 中文（繁體） ∙ +/−

Original upload log

This image is a derivative work of the following images:

File:Pythagoras_similar_triangles.PNG licensed with Cc-by-sa-3.0, GFDL
- 2010-05-05T04:59:48Z Brews ohare 960x600 (70261 Bytes) Arcs for angles
- 2010-05-04T23:02:02Z Brews ohare 960x600 (67020 Bytes) Simplify further
- 2010-05-04T22:35:26Z Brews ohare 960x600 (74056 Bytes) Move labels outside triangle
- 2010-05-04T22:26:16Z Brews ohare 948x598 (71817 Bytes) spacing of elements
- 2010-05-04T22:20:25Z Brews ohare 948x597 (71826 Bytes) Reduce clutter
- 2010-05-04T21:43:58Z Brews ohare 986x693 (98895 Bytes) larger angle labels; right angle; altitude heavier
- 2010-05-04T19:37:49Z Brews ohare 988x695 (98337 Bytes) larger labels
- 2010-05-04T19:26:26Z Brews ohare 986x693 (94166 Bytes) enlarge labels
- 2010-05-04T19:18:46Z Brews ohare 970x673 (90356 Bytes) {{Information |Description={{en|1=Similar triangles for Pythagoras' theorem}} |Source={{own}} |Author=[[User:Brews ohare|Brews ohare]] |Date=2012-05-04 |Permission= |other_versions= }} [[Category:Pythagorean theorem]]

Uploaded with derivativeFX

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	12:17, 10 April 2012	811 × 660 (10 KB)	Gauravjuvekar	validation
	14:50, 17 March 2012	811 × 660 (15 KB)	Gauravjuvekar	Reverted to version as of 14:18, 17 March 2012, arrows
	14:32, 17 March 2012	512 × 417 (8 KB)	Gauravjuvekar	Removing line-height attribute (11 times)
	14:22, 17 March 2012	512 × 417 (8 KB)	Gauravjuvekar	validation
	14:18, 17 March 2012	811 × 660 (15 KB)	Gauravjuvekar	== {{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:Pythagoras_similar_triangles.PNG:...