Question

Geometry review
plz help

Answer 1

Prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. Be sure to create and name the appropriate geometric figures.

Answer 2

@Vocaloid @dude

Answer 3

Ok no problem thanks voca

Answer 4

alright, turns out they're looking for a different method, start by constructing two right triangles like so:

Answer 5

Oh boy

Answer 6

we label the angles A and B like so, then you can demonstrate that both triangles are 30-60-90 triangles with a bit of basic algebra (each triangle must sum up to 180) so they are similar

Answer 7

now we set up a proportion where

short leg/hypotenuse of the entire big triangle = short leg/hypotenuse of the blue triangle so

b/(d+e) = d/b

cross multiplying gives us

b^2 = d(d+e)

then we can set up another proportion where long leg/hypotenuse of the big triangle = long leg/hypotenuse of the green triangle

cross multiplying the equations gives us:

e/a = a/(d+e)

a^2 = e/(d+e)

replacing d + e with c gives us

b^2 = dc

a^2 = ec

adding these together gives us

a^2 + b^2 = dc + ec

factoring the right side gives us

a^2 + b^2 = c(d+e)

replacing the d + e with c gives us

a^2 + b^2 = c^2 --> proving the theorem

lmk if there's anything that was unclear

Answer 8

Thats alot of info for me to process gimme a minute xD thanks again @Vocaloid