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.

- anonymous

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- anonymous

by AA similarity postulate:
â–³ADBâˆ¼â–³BDCâˆ¼â–³ABC
therefore the sides of the triangles are proportional:
AD/AB = AB/AC
BC/AC = DC/BC
By cross multiplication we have the following equations:
AD * AC = AB * AB
AC * DC = BC * BC
Which is the same as:
AD * DC = BD^2
AD * AC = AB^2
AC * DC = BD^2
Add the two equations:
AD * AC AC * DC = AB^2 BC^2
By the distributive property:
AC(AD DC) = AB^2 BC^2
but by construction AD DC = AC...so we have:
AC * AC = AB^2 BC^2
Which is equivalent to:
AB^2 BC^2 = AC^2
Which is what we want to prove.

- anonymous

that is what i have... i just want to make sure im right..

- anonymous

i love this i got it

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## More answers

- anonymous

well a^2+b^2=c^2 so is that what you have as your first step

- anonymous

im guessing..the coding got messed up and idk what it is now XD

- anonymous

you used the distubitive propery i think

- anonymous

So do u think that is a correct proof to answer the question?

- anonymous

i'm guessing, probably

- anonymous

no do u know how to do the theroum

- anonymous

not at all

- anonymous

awwww ship

- anonymous

wanna learn

- anonymous

...i guess?

- anonymous

i just wanted to know if what i did was right or not..

- anonymous

XD

- anonymous

well not u did the distributive property the Pythagorean Theorem is a^2+b^2=c^2 ill give u the site to understand it better

- anonymous

https://en.wikipedia.org/wiki/Pythagorean_theorem go to this site

- anonymous

So should i just change the top line to the "a^2+b^2=c^"??

- anonymous

then your answer will be all wrong

- anonymous

0-0 okay.. then help me re-do it?

- anonymous

ight

- anonymous

Awesome :D

- anonymous

@teagirl7630

- anonymous

so as you know a^2+b^2=C^2

- anonymous

okay, so that's how we begin?

- anonymous

yes

- anonymous

alright

- anonymous

What's next?

- anonymous

it A

- anonymous

then on your tiangle it shows all the and god for flam it love2hot2 and it will say what A, B or c is

- anonymous

ok

- anonymous

...huh?

- anonymous

gtg ill message you

- anonymous

.-. mmkay

- anonymous

yeah

- ybarrap

I'm doing this because I'm not sure how to read what you wrote, so we are starting from scratch. And if you know what to do next. Just do it.

- anonymous

not really.. i think i just need the two colomn proof..but im not sure how to do it correctly.

- ybarrap

Follow my steps here in the order I show, referring to the diagram.
|dw:1437175072230:dw|
We use similarity of 3 triangles to prove.
Does this make sense?

- ybarrap

|dw:1437175582716:dw|