- 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
- 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)
CHAPTER 5
your geometry toolbox
Your Geometry Toolbox
You’ve got Chapter 5 under
your belt and now you’ve
added properties of triangles
to your toolbox. For a complete list
of tool tips in the book, head over to
www.headfirstlabs.com/geometry.
Ar
ea =
∏
r
2
Circumf
er
enc
e
=
∏D
= 2
∏
r
Sec
t
or ar
ea =
∏
r
2
x
Sector angle
360
R
adius =
diameter
2
Arc length =
2
∏r x
Sector angle
360
234 Chapter 5
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