Head First 2D Geometry

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the pythagorean theorem

The Pythagorean Theorem: a

2

+ b

2

= c

2

This pattern is known as The Pythagorean Theorem. Using it you

can find out whether the corner opposite the longest side of a triangle is

acute, obtuse, or a right angle. In words, the theorem is usually written:

The sum of the squares of the legs of a right

triangle is equal to the square of the hypotenuse.

The “hypotenuse” is the

longest side.

These other two

sides are called “legs.”

This is how it’s written as a formula.

So we don’t need to know them

all in advance? We can check jumps

as we go? Perfect—because I’ve

just told everybody we’re setting up a

competition on one of our courses!

a

a

2

+ b

2

> c

2

c

b

a

a

2

+ b

2

< c

2

c

b

a

2

+ b

2

= c

2

a

c

b

For an OBTUSE triangle:

For an ACUTE triangle:

Author’s note: In British

English, it’s known as

Pythagoras’ Theorem.

132 Chapter 3

skate ramp magnets

Skate Ramp Magnets

Sam’s sketched out a rough design for the competition course. She wants

three different sets of ramps for the skaters to demo their skills on—one

with a gap to jump and two with joining rails to slide on.

Using the Pythagorean Theorem and the construction kit magnets, work

out where each part needs to go to complete the course design. Use each

part exactly once.

6

5

Less than 11 wide

More than 11 wide

8

Less than 11 wide ...