Question

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 1

by AA similarity postulate:
△ADB∼△BDC∼△ABC
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.

Answer 2

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

Answer 3

i love this i got it

Answer 4

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

Answer 5

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

Answer 6

you used the distubitive propery i think

Answer 7

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

Answer 8

i'm guessing, probably

Answer 9

no do u know how to do the theroum

Answer 10

not at all

Answer 11

awwww ship

Answer 12

wanna learn

Answer 13

...i guess?

Answer 14

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

Answer 15

XD

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

then your answer will be all wrong

Answer 20

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

Answer 21

ight

Answer 22

Awesome :D

Answer 23

@teagirl7630

Answer 24

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

Answer 25

okay, so that's how we begin?

Answer 26

yes

Answer 27

alright

Answer 28

What's next?

Answer 29

it A

Answer 30

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

Answer 31

ok

Answer 32

...huh?

Answer 33

gtg ill message you

Answer 34

.-. mmkay

Answer 35

yeah

Answer 36

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.

Answer 37

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

Answer 38

Follow my steps here in the order I show, referring to the diagram.


We use similarity of 3 triangles to prove.

Does this make sense?