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. This figure does not need to be submitted

Answer 1

@AlexandervonHumboldt2

Answer 2

yeah

Answer 3

Can you help me?

Answer 4

yes

Answer 5

Draw right triangle ABC by Construction. 2) Draw altitude CD with length h by Construction. 3) Let segment AC = b, segment CB = a, segment AB = c, segment AD = x, and segment DB = y by Labeling. 4) y + x = c by the Segment Addition Postulate. 5) c/a = a/y and c/b = b/x by the Pieces of Right Triangles Similarity Theorem. 6) b² = cx by the Cross Product Property and a² = cy by the Cross Product Property. 7) a² + b² = cy + b² by the Addition Property of Equality. 8) a² + b² = cy + cx by Substitution. 9) a² + b² = c times the quantity y + x, by the Distributive Property of Equality. 10) a² + b² = c * c by Substitution. 11) a² + b² = c² by Multiplication.]

Answer 6

Why is there all them boxes? And is that the answer?
@AlexandervonHumboldt2

Answer 7

oh nevermind about the boxes. lol

Answer 8

i just need to tell that my computer always lose connection andi ofthen need restart so i may be offline for some minutes

Answer 9

um just to shom steps ha

Answer 10

One way to find the area of the outer square is the obvious way \((x+y)^2\)

Another way is to add up the area of the triangles and the inner square

\(4*\frac{1}{2}xy+c^2=2xy+c^2\)

setting these two areas that are equal to each other we get

\((x+y)^2=2xy+c^2\\x^2+2xy+y^2=2xy+c^2\\x^2+y^2=c^2\)

Answer 11

Thanks.

Answer 12

welll thats another way but not using similar triangles but it is good also

Answer 13

If you need to use triangles only then simply turn the squares into two equal triangles

Answer 14

you will get (1/2)(x+y)^2+(1/2)(x+y)^2=(x+y)^2

Answer 15

same thing for the inside square...

Answer 16

\(\frac{1}{2}(x+y)^2+\frac{1}{2}(x+y)^2=4\frac{1}{2}xy+\frac{1}{2}c^2+\frac{1}{2}c^2\\x^2+y^2=c^2\)

Answer 17

that way is wall with triangles

Answer 18

Thanks @zzr0ck3r you explained it very well. I see how both can be right now.

Answer 19

yeah yeah , I was just waiting until the other person was done, to show you another way

There are over 100 proofs for this.

The 8th president of the united states of America is responsible for one of them!

Answer 20

then he got shot ;(