Omar is setting up a proof of the pythagorean theorem. he draws a scalene right triangle and plans to use similar triangles in his proof. what else should he draw?

Step-by-step explanation:  He has to draw a perpendicular line (dot line in Annex) from A vertex  to side  BC. Doing that, he will build two additional triangles ADB  and  ADC.

We can show these  three triangles are similar.

In triangle ABC angles  

∠ BAC  is a right angle (90° )

Then we can call ∠ ACB   =  α     and therefore  ∠ ABC  =  90 -  α

Since the sum of internal angles in any triangle is 90°

Now in Triangle  ADB

∠ ADB   is a right angle (90° )

Sides of ∠ BAD are perpendicular sides of ∠ ABC  according to

AB ⊥ AC    and    BC  ⊥  AD   Then ∠ BAD  =   ∠ ABC  =  90° -  α

And triangle  ADC

∠ ADC   is a right angle (90° )

∠ ACB  is common to both triangles ( the original one and triangle ACD )

Then we have shown that the three triangles are similar

Δ ABC ≈ Δ ADC ≈ Δ ADB

Therefore  we can work with sides proportionality:

b /a   = a - x / b      or      b²  =  a ( a - x )     b²  = a²  - ax    (1)

And

c / x  = a /c    ⇒  c²  =  ax      (2)

Then  adding  (1)  and (2)

b²  +  c²   =  a²

What we want to show

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