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by Dawn Griffiths, Stray
Head First 2D Geometry
Advance Praise for Head First 2D Geometry
Praise for other Head First books
Copyright
Dedication
The Authors
Table of Contents (1/2)
Table of Contents (2/2)
How to Use this Book: Intro
Who is this book for?
We know what you’re thinking.
And we know what your brain is thinking.
Metacognition: thinking about thinking
Here's what WE did:
Read Me
The technical review team
Acknowledgments
Safari® Books Online
Chapter 1: Finding Missing Angles: Reading Between the Lines
There’s been a homicide
In the ballistics lab you’ve got to cover all the angles
Do the angles between Benny, Micky, and the bullet match up?
Right angles aren’t always marked with numbers
Angles can be made up of other, smaller angles
Complementary angles always add up to a right angle (90º)
Right angles often come in pairs
Angles on a straight line add up to 180º
Pairs of angles that add up to 180º are called supplementary angles
Vertical angles are always equal
The corner angles of a triangle always add up to a straight line
Find one more angle to crack the case
Something doesn’t add up!
If it doesn’t all add up, then something isn’t as it seems
You’ve proved that Benny couldn’t have shot Micky!
We’ve got a new sketch—now for a new ballistics report
We need a new theory
Work out what you need to know
Tick marks indicate equal angles
Use what you know to find what you don’t know
The angles of a four-sided shape add up to 360º
Parallel lines are lines at exactly the same angle
Parallel lines often come with helpful angle shortcuts
Great work—you cracked the case!
Your Geometry Toolbox
Chapter 2: Similarity and Congruence: Shrink to Fit
Welcome to myPod! You’re hired
Liz wants you to etch her phone
The designer noted some of the details
The design tells us that some triangles are repeated
Similar triangles don’t just look the same
To use similarity, you need to be able to spot it
You can spot similar triangles based on just two angles
Employee of the month already?
You sketch it—we’ll etch it!
Fire up the etcher!
The boss isn’t happy, but at least you’re not fired…
It’s a problem of scale…
Complex shapes can be similar, too
You sketch it—we’ll etch it (to fit)
Liz is back with a special request
Similar shapes that are the same size are congruent
Use what you know to find what you don’t know (1/2)
Use what you know to find what you don’t know (2/2)
Ratios can be more useful than sizes
Ratios need to be consistent
Your new design ROCKS!
Your Geometry Toolbox
Chapter 3: The Pythagorean Theorem: All the Right Angles
Giant construction-kit skate ramps
Standard-sized-quick-assembly-what?!?
The ramps must have perpendicular uprights
You can use accurate construction to test ramp designs on paper (1/2)
You can use accurate construction to test ramp designs on paper (2/2)
Not all lengths make a right triangle
You can explore a geometry problem in different ways
In geometry, the rules are the rules
Any good jump has some similar scaled cousins
The lengths of the sides are linked by a pattern
The square of the longest side is equal to the squares of the other two sides added together
The Pythagorean Theorem: a² + b² = c² (1/2)
The Pythagorean Theorem: a² + b² = c² (2/2)
Using Kwik-klik skate ramps is definitely the right angle!
A longer rope swings further and lower
So, how far can you swing on a six-meter rope?
Your rope swing is perfect
Your Geometry Toolbox
Chapter 4: Triangle Properties: Between a Rock Show and a Triangular Place
Everybody loves organizing a rock festival
First we need to pick a venue
Fencing costs money
Does a bigger perimeter mean a bigger area?
How many people can each venue hold?
A triangle fits inside a bounding rectangle (1/2)
A triangle fits inside a bounding rectangle (2/2)
The area of a triangle = 1/2 base × height
You’ve got $11,250 to spend
All speakers are not created equal
So what are you looking for in your speakers?
The ideal speakers are wider and longer than the venue…but only by a little
100m will do, but can you rent the 60° speaker?
The 60° speakers are spot on
All that’s left is to pick a spot for the drinks stall
A triangle has more than one center
The center of a triangle can be outside the triangle
Let’s put the drink stall at the centroid
The rock festival is ready!
The people behind the drinks stall won’t see the stage…
You need a screen for less than $1,440
Will the special offer screen still do the job?
You can find area from sides using Hero’s formula
Hero’s formula and “1/2 base × height” work together
The rock festival is gonna…rock!
Your Geometry Toolbox
Chapter 5: Circles: Going Round and Round
It’s not just pizza—it’s war!
How does MegaSlice’s deal measure up?
The diameter of a circle is twice its radius
How do slices compare to whole pizzas?
Sectors of a circle have angles totaling 360°
MegaSlice’s $10 deal is a con!
Pepperoni crust pizza—but at what price?
The pepperoni perimeter is 3 (and a bit) times diameter
Mario wants to put your pepperoni crust pricing formula to the test
The customers are always fussy
An arc is a section of the circumference
Mario’s business is booming!
But MegaSlice is at it again...
We need to find the area of the two pizza deals
Each sector (slice) is a triangle (kind of)
Area of a circle = πr²
Mario’s pizza is here to stay
Your Geometry Toolbox
Chapter 6: Quadrilaterals: It's Hip to be Square
Edward’s Lawn Service needs your help
Your first lawn
The lawn is a parallelogram
Let’s split the parallelogram
Business is booming!
If you don’t like what you’re given, change it
But people are upset with Ed’s prices…
Let’s compare the two lawns
The lawns need edging, too
Same shape, different perimeters
Edward changed his rates…
…and the customers keep flooding in
Use diagonals to find the area of the kite
Landowners, unite
There are some familiar things about this shape
Calculate trapezoid area using base length and height
The quadrilateral family tree
You’ve entered the big league
Your Geometry Toolbox
Chapter 7: Regular Polygons: It's All Shaping Up
We need to choose a hot tub
All the hot tubs are regular polygons
Regular polygons have equal sides and angles
Butt-space is all about perimeter
Is 3 cubic meters of water a lot or a little?
Hot tub volume is area × depth
The hot tub’s area must be 6m²
Which hot tub shape gives the most butt-space?
Work backward from area to find butt-space
Is 19.6 butts a lot or a little?
The square tub beats the circle tub
Two tubs down, five to go
You’ve found the formula for the area of an equilateral triangle
Keep track of complex comparisons with a table (1/2)
Keep track of complex comparisons with a table (2/2)
Chop the polygons into triangles
What do we need to know about the polygon triangles?
The circles give us the properties we need
Polygon area = 1/2 perimeter × apothem
More sides = fewer butts
Rock stars—high maintenance?
Great tub choice!
But what about dimensions?
It’s time to relax in the hot tub!
Your Geometry Toolbox
Leaving town…
It’s been great having you here in Geometryville!
Index (1/2)
Index (2/2)
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Advance Praise for Head First 2D Geometry
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