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Head First 2D Geometry

Book Description

Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and nail your class exams along the way. We think your time is too valuable to waste struggling with new concepts. Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, Head First 2D Geometry uses a visually-rich format designed for the way your brain works, not a text-heavy approach that puts you to sleep.

Table of Contents

  1. Advance Praise for Head First 2D Geometry
  2. Praise for other Head First books
  3. Copyright
  4. Dedication
  5. The Authors
  6. Table of Contents (1/2)
  7. Table of Contents (2/2)
  8. How to Use this Book: Intro
    1. Who is this book for?
    2. We know what you’re thinking.
    3. And we know what your brain is thinking.
    4. Metacognition: thinking about thinking
    5. Here's what WE did:
    6. Read Me
    7. The technical review team
    8. Acknowledgments
    9. Safari® Books Online
  9. Chapter 1: Finding Missing Angles: Reading Between the Lines
    1. There’s been a homicide
    2. In the ballistics lab you’ve got to cover all the angles
    3. Do the angles between Benny, Micky, and the bullet match up?
    4. Right angles aren’t always marked with numbers
    5. Angles can be made up of other, smaller angles
    6. Complementary angles always add up to a right angle (90º)
    7. Right angles often come in pairs
    8. Angles on a straight line add up to 180º
    9. Pairs of angles that add up to 180º are called supplementary angles
    10. Vertical angles are always equal
    11. The corner angles of a triangle always add up to a straight line
    12. Find one more angle to crack the case
    13. Something doesn’t add up!
    14. If it doesn’t all add up, then something isn’t as it seems
    15. You’ve proved that Benny couldn’t have shot Micky!
    16. We’ve got a new sketch—now for a new ballistics report
    17. We need a new theory
    18. Work out what you need to know
    19. Tick marks indicate equal angles
    20. Use what you know to find what you don’t know
    21. The angles of a four-sided shape add up to 360º
    22. Parallel lines are lines at exactly the same angle
    23. Parallel lines often come with helpful angle shortcuts
    24. Great work—you cracked the case!
    25. Your Geometry Toolbox
  10. Chapter 2: Similarity and Congruence: Shrink to Fit
    1. Welcome to myPod! You’re hired
    2. Liz wants you to etch her phone
    3. The designer noted some of the details
    4. The design tells us that some triangles are repeated
    5. Similar triangles don’t just look the same
    6. To use similarity, you need to be able to spot it
    7. You can spot similar triangles based on just two angles
    8. Employee of the month already?
    9. You sketch it—we’ll etch it!
    10. Fire up the etcher!
    11. The boss isn’t happy, but at least you’re not fired…
    12. It’s a problem of scale…
    13. Complex shapes can be similar, too
    14. You sketch it—we’ll etch it (to fit)
    15. Liz is back with a special request
    16. Similar shapes that are the same size are congruent
    17. Use what you know to find what you don’t know (1/2)
    18. Use what you know to find what you don’t know (2/2)
    19. Ratios can be more useful than sizes
    20. Ratios need to be consistent
    21. Your new design ROCKS!
    22. Your Geometry Toolbox
  11. Chapter 3: The Pythagorean Theorem: All the Right Angles
    1. Giant construction-kit skate ramps
    2. Standard-sized-quick-assembly-what?!?
    3. The ramps must have perpendicular uprights
    4. You can use accurate construction to test ramp designs on paper (1/2)
    5. You can use accurate construction to test ramp designs on paper (2/2)
    6. Not all lengths make a right triangle
    7. You can explore a geometry problem in different ways
    8. In geometry, the rules are the rules
    9. Any good jump has some similar scaled cousins
    10. The lengths of the sides are linked by a pattern
    11. The square of the longest side is equal to the squares of the other two sides added together
    12. The Pythagorean Theorem: a² + b² = c² (1/2)
    13. The Pythagorean Theorem: a² + b² = c² (2/2)
    14. Using Kwik-klik skate ramps is definitely the right angle!
    15. A longer rope swings further and lower
    16. So, how far can you swing on a six-meter rope?
    17. Your rope swing is perfect
    18. Your Geometry Toolbox
  12. Chapter 4: Triangle Properties: Between a Rock Show and a Triangular Place
    1. Everybody loves organizing a rock festival
    2. First we need to pick a venue
    3. Fencing costs money
    4. Does a bigger perimeter mean a bigger area?
    5. How many people can each venue hold?
    6. A triangle fits inside a bounding rectangle (1/2)
    7. A triangle fits inside a bounding rectangle (2/2)
    8. The area of a triangle = 1/2 base × height
    9. You’ve got $11,250 to spend
    10. All speakers are not created equal
    11. So what are you looking for in your speakers?
    12. The ideal speakers are wider and longer than the venue…but only by a little
    13. 100m will do, but can you rent the 60° speaker?
    14. The 60° speakers are spot on
    15. All that’s left is to pick a spot for the drinks stall
    16. A triangle has more than one center
    17. The center of a triangle can be outside the triangle
    18. Let’s put the drink stall at the centroid
    19. The rock festival is ready!
    20. The people behind the drinks stall won’t see the stage…
    21. You need a screen for less than $1,440
    22. Will the special offer screen still do the job?
    23. You can find area from sides using Hero’s formula
    24. Hero’s formula and “1/2 base × height” work together
    25. The rock festival is gonna…rock!
    26. Your Geometry Toolbox
  13. Chapter 5: Circles: Going Round and Round
    1. It’s not just pizza—it’s war!
    2. How does MegaSlice’s deal measure up?
    3. The diameter of a circle is twice its radius
    4. How do slices compare to whole pizzas?
    5. Sectors of a circle have angles totaling 360°
    6. MegaSlice’s $10 deal is a con!
    7. Pepperoni crust pizza—but at what price?
    8. The pepperoni perimeter is 3 (and a bit) times diameter
    9. Mario wants to put your pepperoni crust pricing formula to the test
    10. The customers are always fussy
    11. An arc is a section of the circumference
    12. Mario’s business is booming!
    13. But MegaSlice is at it again...
    14. We need to find the area of the two pizza deals
    15. Each sector (slice) is a triangle (kind of)
    16. Area of a circle = πr²
    17. Mario’s pizza is here to stay
    18. Your Geometry Toolbox
  14. Chapter 6: Quadrilaterals: It's Hip to be Square
    1. Edward’s Lawn Service needs your help
    2. Your first lawn
    3. The lawn is a parallelogram
    4. Let’s split the parallelogram
    5. Business is booming!
    6. If you don’t like what you’re given, change it
    7. But people are upset with Ed’s prices…
    8. Let’s compare the two lawns
    9. The lawns need edging, too
    10. Same shape, different perimeters
    11. Edward changed his rates…
    12. …and the customers keep flooding in
    13. Use diagonals to find the area of the kite
    14. Landowners, unite
    15. There are some familiar things about this shape
    16. Calculate trapezoid area using base length and height
    17. The quadrilateral family tree
    18. You’ve entered the big league
    19. Your Geometry Toolbox
  15. Chapter 7: Regular Polygons: It's All Shaping Up
    1. We need to choose a hot tub
    2. All the hot tubs are regular polygons
    3. Regular polygons have equal sides and angles
    4. Butt-space is all about perimeter
    5. Is 3 cubic meters of water a lot or a little?
    6. Hot tub volume is area × depth
    7. The hot tub’s area must be 6m²
    8. Which hot tub shape gives the most butt-space?
    9. Work backward from area to find butt-space
    10. Is 19.6 butts a lot or a little?
    11. The square tub beats the circle tub
    12. Two tubs down, five to go
    13. You’ve found the formula for the area of an equilateral triangle
    14. Keep track of complex comparisons with a table (1/2)
    15. Keep track of complex comparisons with a table (2/2)
    16. Chop the polygons into triangles
    17. What do we need to know about the polygon triangles?
    18. The circles give us the properties we need
    19. Polygon area = 1/2 perimeter × apothem
    20. More sides = fewer butts
    21. Rock stars—high maintenance?
    22. Great tub choice!
    23. But what about dimensions?
    24. It’s time to relax in the hot tub!
    25. Your Geometry Toolbox
    26. Leaving town…
    27. It’s been great having you here in Geometryville!
  16. Index (1/2)
  17. Index (2/2)