Head First 2D Geometry

the pythagorean theorem

Using Kwik-klik skate ramps is definitely the right angle!

By finding right triangles with whole number ratios between

the lengths of the sides, you’ve managed to build a whole load

of different ramps from the Kwik-klik standard parts. It’s a fast,

cheap, and smart way to build a skate course, and you’re in a

great position to reap the rewards.

That was so easy! I can’t

wait for the next one. Do

you want your cut of the

money now, or should I just

let it pile up for a while?

Unbelievable! Not only did the

course get assembled in a day but

man, it was the hottest street course

we’ve seen in a long time. Some

serious kick-flipping action was had

over some huge jumps, and we just

about tail-slid our way to heaven on

the excellent ramp-and-rail section.

Fran ‘five-oh’ Sampson took the

overall number one spot at the end

of the day, but we were all grinning

like winners thanks to Sam & Co’s

fantastic design-and-build efforts.

> click for pics

you are here 4 137

no dumb questions

 To find the longest side, square the other two sides, add those up, and then find the

square root.

 To find a short side, square the other two sides and subtract one from the other. Make

it a positive number and then find the square root.

 Finding missing sides using the Pythagorean Theorem only works for right triangles.

Q:

But WHY? How come it adds up

like that?

A:That is a very good question and one

which mathematicians and philosophers

have struggled with for centuries.

Unfortunately there’s not always good “why”

reasons in geometry—stuff just IS. The

good news is that it’s very reliable…so

while understanding why the Pythagorean

Theorem works is beyond most of us, at

least we can make good use of it.

Q:

Why is it called The Pythagorean

Theorem? Why not something more

meaningful and easier to spell like

“Right triangle check” theorem?

A:Pythagoras was a Greek guy. He was

first to write down the theorem. That isn’t to

say that nobody had noticed it before, but

he gets the props. Shame he wasn’t called

something easier to spell!

Q:

I tried to use the Pythagorean

Theorem to find a missing short side,

and I was stuck trying to find the square

root of a negative number. What should

I do?

A:You’ve probably got your legs and

your hypotenuse mixed up. Try to redo

your subtraction the other way round. This

should give you a positive number, and

you’ll be able to find the square root.

Q:

So is “c” always the hypotenuse?

A:The Pythagorean Theorem uses “c”

for the hypotenuse and “a” and “b” for the

legs. Of course we know that algebra is just

a tool for describing a pattern, and in this

case, the pattern is what’s important: the

Q:

Do all triangles have a

hypotenuse? What if I have two long

sides of equal length and one short

side? Which is the hypotenuse?

A:Only right triangles officially have a

hypotenuse. And if you’ve got two sides

equally long, and one shorter one, your

triangle can’t have a right angle, because it

would fail the c

2

= a

2

+ b

2

test, whichever of

your longer sides you decided was “c”.

But don’t think you can’t use the

Pythagorean Theorem for triangles that

don’t have a right angle…it’s just takes a

little more thought to apply it. (More on that

in a minute.)

longest side squared equals the other

two sides squared. So, if you get mixed

up about your a, b, and c, think about what

the pattern behind that formula is, and go

from there.

OMG! Come read this

email—this is so cool…

you won’t believe it!

138 Chapter 3