kileqeleq a pacun ta tinagiljan a sinikipukeljang Sasusuan ni pitaguras

[[File:Pythagorean.svg|thumb|right|250px|sasusuan ni pitaguras]]
madjaludjalu manu pazangal a pinasusuan mavan aicu '''sasusuan ni pitaguras(畢氏定理)''' (Pythagorean theorem) a sikinemeneman tua vavuduan/tatideqan nua mareka vecik. makaya sinivecik sa papukeljang a ''a'' katua ''b'' tua drusa a gidigidian nua ta tjelu a putung, sa tja sinivecik ''c'' taza calisilisian. a tja kineljang aicu a sasusuan ni pitaguras mavan a sisupusupu sa paseljang matu:<ref>Judith D. Sally; Paul Sally (2007). [https://books.google.com.tw/books?id=nHxBw-WlECUC&pg=PA63&redir_esc=y#v=onepage&q&f=false "Chapter 3: Pythagorean triples".] Roots to research: a vertical development of mathematical problems. American Mathematical Society Bookstore. p. 63. ISBN 978-0-8218-4403-8.</ref> 
:<math> a^2 + b^2 = c^2. </math>

==pinapungadan==
aicu a sususuan a pinapungadan ti piaguras a nasemupu a segeris a kinasicuayan. pasusangas a 1,000 a cavilj tazua, izua za sisupusupu a kineljangan nua caucau i kacauan. ljakua aicu a tja sinipapukeljang a ngadan taicu a sasusuan ni pitaguras tucu.

==sinisupuan==
nu namapacunan a sinivecikan a '''''C''''' a tja sipakeljang tua cacalisian nua ta tjelu a putung, sa pakatua zuma a gidigidian nua za tjelu a putung, izua za sinivecikan a '''''A''''' katua '''''B''''' a sipakeljang, mavan aicu a tja sinipakeljangan a sinisupuan nua sasusuan ni pitaguras:
: <math>a^2 + b^2 = c^2 .</math>
nu namasan aicu a tja kineljangan a laladruqan nua A katua B, manu aicu a tja sisupusupu:
: <math> c = \sqrt{a^2 + b^2}. </math>
nu nakemeljang itjen ta laladruqan nua '''''C''''' a cacalisian katua tailj a gidigidian ('''''A''''' ka na ika '''''B'''''), manu aicu a tja sisupusupu tua laladruqan nua zumanga a gidigidian:
: <math>a = \sqrt{c^2 - b^2} </math>
ka na ika mavan aicu a maumalj a sinisupuan:
: <math>b = \sqrt{c^2 - a^2}. </math>

saka, aicu a tja kineljang tu nu kemeljang itjen ta laladruqan nua matjadrusa a gidigidian nua ta tjelu a putung, maqatitjen a semupu sa kemeljang tua laladruqan nua sikamasantjelulj a gidigidian.
==pinakasaluan==
===sipatjavat tua pakasalu===
[[File:Pythagoras algebraic2.svg|right|150px]]
a tja sipakasalusalu a masan sepatj a tjelu a putung a pinapeseljang. sa paseljang itjen tua aicu a tjelu a putung itua ta sepatj a putung matu tja mapacuanan taicu a vecik i pasanavalj. a tja sipatjavatan aicu '''''C''''' a tja sipakeljang tua gidigidian nua za sepatj a putung.<ref>Alexander Bogomolny. [http://www.cut-the-knot.org/pythagoras/index.shtml#4 "Cut-the-knot.org: Pythagorean theorem and its many proofs, Proof #4".] Cut the Knot. Retrieved 4 November 2010.</ref> nu pasuvililj, izua tjaqaca a sepatj a putung tuki tja kineljang aicu a ''a'' + ''b'' aza gidigidian, saka sikeljangan tua tatideqan naza sepatj a putung aza sisupuan a (''a'' + ''b'')<sup>2</sup>. penaqulid a patjeseljaseljang a tja mapacunan a laludraqan a cacalisian nua matjasepatj a tjelu a putung a katagiljan tua laladruqan a gidigidian nua sepatj a putung nu tjaivililj. a tja sipatjavatjavat mavan cu a '''''C''''' tua za laludraqan.
:<math>(b+a)^2 = c^2 + 4\frac{ab}{2} = c^2+2ab,</math>
a pasuvililj avan cu a masan italj a sisupuspu:
:<math>c^2 = (b+a)^2 - 2ab = b^2+2ab+a^2-2ab = a^2 + b^2.</math>
inka maljian mavan cu a masan italj a sipakasalusalu aza pinaseljangan a masan sepatj a tjelu a putung a pasanavalj (''right triangle''). a tja sipatjavat a '''''a''''', '''''b''''' katua '''''c''''' taza gidigidian. pinitaladj aza sepatj a tjelu a putung tua ta sepatj a putung. a tja sipatjavat tua laladruqan a gidigidian nua za sepatj a putung a '''''c'''''.<ref>Alexander Bogomolny. [http://www.cut-the-knot.org/pythagoras/index.shtml#3 "Cut-the-knot.org: Pythagorean theorem and its many proofs, Proof #3".] Cut the Knot. Retrieved 4 November 2010.</ref> ika maljian a tatideqan nua za tjelu a putung tua tatideqan a <math>\tfrac12ab</math>. saka tja sinipapukeljang a ''b'' − ''a'' tua gidigidian nua masan italj a kedrian a sepatj a putung; a tja kineljang a (''b'' − ''a'')<sup>2</sup> tua tatideqan nua za sepatj a putung. a tjaivililj a tja sipapukeljang tua tatideqan nua tjaqaca a sepatj a putung aicu a sisupusupu sa paseljang matu: 
:<math>(b-a)^2+4\frac{ab}{2} = (b-a)^2+2ab = b^2-2ab+a^2+2ab = a^2+b^2. </math> 
manu tja kineljang taicu a '''''c''''' a laladruqan a gidigidian nua sepatj a putung; aza '''''c'''''<sup>2</sup> a tja sipapukeljang tua tatideqan nua za sepatj a putung. saka, mavan cu a tja sisupusupu sa paseljang:
:<math>c^2 = a^2 + b^2. </math>

==kaizuan==