#1**+2 **

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

CPhill
Aug 31, 2018