Pyhtagoras' Theorem (Theorem 10)

Blue_Seas

Anyone who has the New Concise Maths 2 book could you tell me if the 'Alternative Proof' for Theorem 10 is correct? Some parts are confusing and don't add up to me but then again it could just be going over my head

I'd hate to learn it off though and the examiner mark it wrong because of what's printed wrong in the book (my teacher said that they printed Theorem 9 wrong so I'm cautious).

suitcasepink

Hey I have photocopied sheets of it so Idk what book its from but Im almost 100% that theres mistakes in letters, there was in the previous theorem..

So yea Im learning a whole new phrasing of pythag the night before -_-

Blue_Seas

But if you fail Maths at least you can say "I know what it was, the stupid Theorem I got was photocopied wrong and lost me all my marks!"
But yeah.. anyone heard of proof-reading?

I'm just learning it as is and hope for the best :S

I learned this one today. Both versions I had (Texts and Tests 2 and a photocopied hand-out) both seemed to be wrong. I learned it however so if you type out what you have line by line I could proof read it if you wanna

suitcasepink

Deleted User wrote: »

I learned this one today. Both versions I had (Texts and Tests 2 and a photocopied hand-out) both seemed to be wrong. I learned it however so if you type out what you have line by line I could proof read it if you wanna

Texts and texts is wrong?

Aww ****e
Its the proof yea? Ill type it out in a sec, think I know where its wrong but cant correct it..

Vivara

Being the extremely nice person I am, I did out a version that I've been using for the past few months. It's based on one in Text & Test 2, but I rotated the triangles to make it easier. Got full marks in my pre-exam with this and in our last theorem test, my teacher didn't seem to find any problems. Added some notes as well as it can be confusing seeing where things come from.

View the attachment to see!

Regards,
Ed.

EDIT: Amended to correct version!

Vivara

deise_girl wrote: »

Texts and texts is wrong?

Aww ****e
Its the proof yea? Ill type it out in a sec, think I know where its wrong but cant correct it..

No it's not wrong. It's a bit confusing, though. See my post above.

suitcasepink

Proof:
In triangles abc and dba
|<1| = |<1| common
|<2| = |<3| = 90 construction
therefore triangles abc and dba are similar
therefore |ab|/|bc| = |bd|/|ab| corresponding sides in proportion
therefore |ab|2(squared) = |bc|.|bd| (1) cross multiply
similarly triangle abc and dac are similar
and |ac|2 = |bc|. |dc| (2)
Adding (1) and (2)
|ab|2 + |ac|2 = |bc|. |bd| + |bc|. |dc|
= |bc|(|bd| + |bc| + |dc|)
= |bc|. |bc|
= |bc|2
therefore |bc|2 = |ab|2 + |ac|2
Correct plz

Deise. That seems perfect to me
Vivara, not to throw you into a tizzy or anything but in your first proof, you have ab/bd = bc/ab yet when you cross multiply, your bd turns into an ad. That's the problem

deise_girl

deise_girl wrote: »

Proof:
In triangles abc and dba
|<1| = |<1| common
|<2| = |<3| = 90 construction
therefore triangles abc and dba are similar
therefore |ab|/|bc| = |bd|/|ab| corresponding sides in proportion
therefore |ab|2(squared) = |bc|.|bd| (1) cross multiply
similarly triangle abc and dac are similar
and |ac|2 = |bc|. |dc| (2)
Adding (1) and (2)
|ab|2 + |ac|2 = |bc|. |bd| + |bc|. |dc|
= |bc|(|bd| + |dc|) <---- Fixed here, bc is taken out as common factor
= |bc|. |bc| <

---

bd + dc = bc from original diagram
= |bc|2
therefore |bc|2 = |ab|2 + |ac|2
Correct plz

Just some little things I actually just noticed :rolleyes: And added in notes that the examiner might need to see :cool:

suitcasepink

Thank yee all soo soo much!
Of course Im only learning theorems now -_-

I wouldn't stress too much, learn the pythagoras and maybe a few complicated ones. Knowing how to use formulae and where etc. will get you most marks
And of course my golden tip. Always take a guess or at least write down the formula/ diagram for the theorem you try prove because that gets attempt marks (for the theorem at least)

Vivara

Deleted User wrote: »

Vivara, not to throw you into a tizzy or anything but in your first proof, you have ab/bd = bc/ab yet when you cross multiply, your bd turns into an ad. That's the problem

Stupid typo. Amended above. See image here.

Ed.

Cool Just pointed it out because you clearly know it so no point losing the mark for a slip

Vivara

Deleted User wrote: »

Cool Just pointed it out because you clearly know it so no point losing the mark for a slip

I wouldn't have lost it, LOL... I don't memorise my theorems, I just look at the diagrams and am able to prove it then. It's the way our teacher taught us. So I didn't memorise the error — that would be funny, LOL.

Ed.

Vivara

Vivara wrote: »

I wouldn't have lost it, LOL... I don't memorise my theorems, I just look at the diagrams and am able to prove it then. It's the way our teacher taught us. So I didn't memorise the error — that would be funny, LOL.

Ed.

Me either I know a lot of people who do, especially pythagoras since as you say Text and Tests is confusing to understand. Good to know the logic behind them as if you don't, you don't recognise the errors in samples