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Does anyone have any idea about geometric proof? I would like a definition and equation example. Please and thank you! smiley By the way, I've never seen the concept before, so I would like an in-depth disscussion on the subject.angry

OwenT154  Aug 31, 2018
edited by OwenT154  Aug 31, 2018
 #1
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Here's a geometric proof of the Pythagorean Theorem using similar triangles :

 

 

 

Let  ABC  be a righ triangle with a right angle at C

And CD is an altitude  with right angles ADC  and BDC

 

We want to prove that  AC^2  + BC^2 =  AB^2

 

So...looking at triangles ABC  and ADC

Angle A  = angle A

Angle ACB  = angle CDA

So...by AA  congruency.....Δ ACB ~Δ ADC  →  AC /AB  = AD/ AC  →  AC^2  = AB * AD

 

Similary  Δ ACB ~ ΔCDB → AB / BC = BC / DB  →  BC^2  = AB * DB

 

So

 

AC^2  + BC^2  = AB* AD   + AB * DB

AC^2 + BC^2  = AB ( AD + DB)

AC^2 + BC^2  = AB (AB)

AC^2 + BC^2  = AB^2

 

 

cool cool cool

CPhill  Aug 31, 2018

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