#### alevelsprivately

##### New member

- Joined
- Aug 12, 2019

- Messages
- 2

This is my first post on this website, so lets stick to constructive criticism.

Thanks

I was trying to prove Pythagorean Theorem myself, I drew this triangle

(just a reference)

Its basically a right angle triangle with a perpendicular angle bisector.

From here what I do is get divide BC into BD = x and DC = y

Now using trig (stupid for this proof but...)

x = ABsin45 = AB/\(\displaystyle \sqrt{2} \)

y = ACsin45 = AC/\(\displaystyle \sqrt{2} \)

so as BC = x+y

\(\displaystyle BC = (AB + AC)/ \sqrt{2} \)

now squaring both sides

\(\displaystyle BC^2 = (AB+AC)^2/2 \)

or more generally

\(\displaystyle h^2 = (a + b)^2/2 \)

Now out of curiosity I tried this out on the 3-4-5 right angled triangle

and I got

\(\displaystyle \sqrt{(3+4)^2/2}

= 4.95

\)

which is pretty close to 5

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Now my question is,

Can anyone explain me what relationship have I found between these variables or am I just pondering upon a special case

or maybe just a bad way to prove Pythagorean theorem. I am pretty confused as to what this is.

Also, if I have gone wrong somewhere please correct me.

Thanks again for all the help