# HEAD FIRST 2D GEOMETRY PDF

This Repo contain Head First series eBook. Contribute to abhinavkorpal/ head_first_series_books development by creating an account on GitHub. Advance Praise for Head First 2D Geometry “Head First did it again. The ability to make the reader understand, despite. Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? 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.

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Pages: | 166 |

Published (Last): | 09.12.2015 |

ISBN: | 411-2-16167-947-5 |

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Head First 2D Geometry comes with step-by-step, interesting and practical examples, fun design, and a conversational style in our real world. Head First 2D Geometry - dokument [*.pdf] Download at mencosulwiemudd.gq Advance Praise for Head First 2D Geometry “Head First did it again. The ability to . 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.

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. Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more. Start Free Trial No credit card required. Head First 2D Geometry 1 review. View table of contents. Start reading. Book Description Having trouble with geometry? Intro Who is this book for? And we know what your brain is thinking. Karen Montgomery Production Editor: Rachel Monaghan Indexer: Angela Howard Proofreader: Nancy Reinhardt Page Viewers: November First Edition.

Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. While every precaution has been taken in the preparation of this book, the publisher and the authors assume no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein. No sheep or triangles were harmed in the making of this book. Com To Mum and Dad for downloading me construction kits. To my fantastic Yorkshire family for endless support, humour, and psychotherapy— I love you even more than I love triangles.

And to triangles and sheep, for making the world a fascinating place to be. Also in loving memory of Peter Lancaster Walker, an unsung hero who made so many things possible. Com viii Lindsey Fallow is a self-confessed geek who has spent the past decade exploring science and technology as a writer, software developer, and TV presenter.

Lindz claims that if she were a superhero, her superpower would be tesselating. Dawn Griffiths started life as a mathematician at a top UK university where she was awarded a first-class honours degree in mathematics. She went on to pursue a career in software development, and she currently combines IT consultancy with writing, editing, and mathematics. Dawn is the author of Head First Statistics, and has also worked on a host of other books in the series, from Networking to Programming.

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She also enjoys traveling, and spending time with her wonderful husband, David. Dawn has a theory that Head First Bobbin Lacemaking might prove to be a big cult hit, but she suspects that Brett might disagree. Reading between the lines 1 2 Similarity and congruence: Shrink to fit 49 3 The Pythagorean Theorem: All the right angles 4 Triangle properties: Between a rock show and a triangular place 5 Circles: Part of the learning especially the transfer to long-term memory happens after you put the book down.

Your brain needs time on its own, to do more processing. If you put in something new during that processing time, some of what you just learned will be lost.

Lots of it. Your brain works best in a nice bath of fluid. Dehydration which can happen before you ever feel thirsty decreases cognitive function. Out loud. Speaking activates a different part of the brain. Better still, try to explain it out loud to someone else. Pay attention to whether your brain is getting overloaded. Your brain needs to know that this matters. Get involved with the stories. Make up your own captions for the photos. Groaning over a bad joke is still better than feeling nothing at all.

Pick up a model kit or some wood and tools and make something really cool! Or work out something you will build one day when you have the time and money. There are no formal proofs in this book. We believe that, for most people, proofs make learning geometry harder than it needs to be. This is just about two-dimensional 2D geometry. We use plain English and not geometry jargon.

We believe your brain needs to see what something is, and figure out why you would even care about it, before you can give it an unfamiliar label.

We encourage you to use real words to describe patterns and not sweat the official formulas too much. Come and talk to us at www. They also give your brain a chance to hook in to the geometry that is all around you in the real world. The redundancy is intentional and important. One distinct difference in a Head First book is that we want you to really get it. For some of them, there is no right answer, and for others, part of the learning experience of the Brain Power activities is for you to decide if and when your answers are right.

In some of the Brain Power exercises, you will find hints to point you in the right direction. For this book we had an amazing group, many of whom have reviewed other Head First books in the past. She is studying nutrition with plans of getting a second degree in nursing. This is her second time reviewing for the Head First series.

David Myers taught college and high school math for 36 years. Since retiring in from a long tenure at The Winsor School in Boston, MA, he has been delighted to start a new completely-for-fun career as a volunteer at his Quaker Meeting and in prisonrelated activities. Currently, he is an instructor of mathematical sciences at Loyola University Maryland and served as department chair of mathematics retired at Hereford High School.

Extra props to her for googling our odd British phrases and sayings to find U. Courtney Nash And to Brett McLaughlin, who started us off on this book, and provided some really kick-ass training on the Head First way and why it rules the world. Also to the folk who rocked training in Boston and added so much to the experience: We heard everybody named in person downloads a copy. To Karen Shaner, who handled the tech-review process, and provided a pep talk when the comments first started coming.

To Lou Barr, for her genius Head First template. And to Scott DeLugan and Sanders Kleinfeld, for once again going above and beyond to get the book out. And for accommodating a year of lost weekends and working-onvacation, and never, ever being intolerant of yet another conversation about triangles.

## Head First 2D Geometry

Work on this book would have been lot harder without my amazing support network of family and friends. And finally: To Bert Bates and Kathy Sierra, for creating the series that changed our lives.

With a subscription, you can read any page and watch any video from our library online. Read books on your cell phone and mobile devices.

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Handsome, rich and single. So yeah, I owed Micky a little money and went out to meet him at some waterfront warehouse. I was gonna pay him, I swear. Bullets travel in straight lines The whole basis of your investigation is something that all bullets have in common: Angles matter Angles are formed where straight lines meet. Because bullets move in straight lines, taking aim really means deciding what the angle is between you and the target. The angle of the shot determines whether the bullet hits or misses the target.

A shot at this angle misses the target. But, they found one important detail: So, to solve the crime, all you have to do is prove that from where Benny was standing to the target Micky , the bullet would have traveled in a straight line that joins up perfectly with the bullet path.

You can see just by looking at it that the line from Benny to Micky and the line for the bullet path join up to make one straight line. Oh, well, we could use a ruler to check it. I bet the chief will say we need to fill them all in. Frank Jill Joe Jill: What if we could find a way to guess some angles based on other angles or something? But that just sounds really inaccurate—not exactly good for our case in court! It sounds like the right kind of approach though.

Instead of drawing a curve, like we do for most angles, we mark it with a square corner. We could also say that one of the lines is perpendicular to the other.

So it turns out that we do have five angles on the sketch after all. A line segment is just a bit of a line with a start and an end. We calculate missing angles rather than measure them. What about all the other lines on the diagram?

The other line segments on the sketch represent things like walls or the path between two points. What we need to find out is whether they join up to form one single straight line. Usually, complementary angles are adjacent next to each other , but they can be any two angles anywhere that add up to 90 degrees.

Hey, you look nice today! Not so bad yourself We say that the angles complement each other. Draw lines to connect up five pairs of complementary angles. Can you work out their complements? Your second answer might be surprising. Complements can never be negative. Did this surprise you? Only acute angles can be complementary.

The angle on a straight line is a half-turn. But what on earth has working out the angle behind the corner of the building got to do with proving that Benny shot Micky all the way over on the other side? Often you need to solve the puzzle piece by piece. It would be great to jump straight to the most important angle—if you even knew what that was—but usually we need to find a bunch of less exciting stuff to help us get there.

You can assume that all the lines shown here are straight. What might this pair of mystery angles a and b from our crime scene sketch add up to? Half a pizza is half a pizza, no matter how you slice it. Some gaps might need more than one magnet to fill them. These two angles must be supplementary.

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Use supplementary angles to find mystery angles a and b. Is there anything surprising about mystery angle a? When two straight lines cross they always create two pairs of equal opposite angles, called vertical angles. Each angle has to form a supplementary pair with either of the angles on the other side of it, so they must be equal.

These two are equal. The supplements must be equal These two are also equal. So if you know …you already know this one, too! Do this! On some scrap paper, draw a triangle using a ruler. Cut the triangle out. Tear the corners off. And then put the three corner pieces together with the points in the middle.

Weird, huh? This is true for every triangle you could possibly draw! Find this last mystery angle to complete your investigation and prove that Benny was the shooter.

They should be is going on. Using the two different methods for finding the mystery angles gives us two different results. And vertically opposite angles are equal, so?

The whole investigation could be compromised by bad math! This is a disaster. How can there be two different answers? Can we fix it? I mean—corners on a triangle always add up to degrees, and vertically opposite angles are always equal.

Those are the rules. I knew we were relying too much on these coincidences. But there was this other guy there, Charlie, inside the building. I think he took a shot at me. I heard a gunshot and breaking glass so I ducked. The bullet hit the car that was parked behind me, and then it sped away. And the chief is on the phone… Great work. This case was a mess before you started working up the ballistics. But who the heck is Charlie?

We do know that the bullet must have traveled in a straight line headed in the direction shown on the sketch, but how it got there is the big question.

Maybe some aliens came down and shot Micky? This is stupid. You can use the statement Benny gave and all the relevant information on the crime scene sketch to guide you. Our points, lines, and angles are still as true as ever.

The bullet hit the car that was parked behind me—it sped away. Using the sketch on the left page, or a blank sheet of paper, can you come up with a new idea about how Micky got shot? A new theory: We have a line from the point where Charlie was standing, through the hole in the window, until it hits the parked car. We also sketched a line moving backward from the bullet, until that hits the parked car, too.

If our theory is true, and Charlie was the shooter, the way the bullet bounced off the car is important. Handy lab guy You guys have a bouncing bullet? Well, whenever we do lab tests on this type of bullet they always bounce out at the same angle as they bounced in on.

Does that help? The bullet bounced equally like this… …not like this. If our bullet bounced as the lab technician described, what do we know should be true about mystery angles x and y? Things that bounce equally bounce like this. Each set of equal angles has a different number of ticks, so you can mark more than one set on the same sketch if you need to. Equal angles Here are some patterns for you to look out for: Angles on a straight line Triangles y Complementar angles Vertical angles On the sketch, mark all the new angles you need to find to solve the crime there are at least We just keep going like we have been.

Oh, good point. Could we add a line of our own and chop the room into two triangles like this? How on earth does that help? Well…at least we know that angles in a triangle add up to degrees. So if we make triangles out of the room, we can keep going like we have been. Like this? OK, but that seems like a lot more work.

Maybe we could try that thing we did with the paper triangle? With the corners? That might show us something about four-sided shapes in general, and we can use that to find those missing angles? What is it that you need to find out about four-sided shapes in order to find the missing angles?

See whether you can figure it out, either by adding up the angles using two triangles, or tearing the corners from a foursided shape to see what they add up to. See whether either method can help you figure it out. To find the missing angles, we need to know what angles in a four-sided shape add up to. A C F One way of finding out is to split the foursided shape into two triangles.

Both methods give us the same answer: Find the mystery angles marked on the crime scene diagram, a, b, c, d, e, f, and the all important angle, g, which lets us work out the bounce angles. Is it possible to tell yet whether Charlie shot Micky? We know these two angles should be equal so we just do minus 32…and then divide by 2 to get 74 degrees!

But how can we check it? But we have the tire tracks—and the angle of one of those. Though not the one on the side that the bullet hit. We use little v-shaped tick marks to indicate sets of parallel lines or line segments on a sketch. Parallel lines can never meet or cross each other, even if you stretch them for miles and miles and miles.

The distance between the lines is constant—they never get closer or farther away. If you have more than one set of parallel lines on the same sketch then you need to use a different number of tick marks on each set to be able to tell them apart. Two different sets of parallel lines. Two sets of vertical angles—notice how one set is exactly the same as the other, so we only have TWO different angles to deal with. This means that you can find more missing angles without doing any math at all—just by recognizing a few patterns.

Find the crucial mystery angles, x and y, and prove once and for all whether Charlie is our shooter. So these sets of vertically opposite angles are the same.

## Head First Python

Nice one—you solved the crime! This means that we have proved that Charlie shot Micky, even if it was Benny he intended to hit! Great work—you cracked the case! Thanks to your work uncovering the angles, the right guy is behind bars. Charlie is gonna be making a lot of license plates Before you collect your bonus and your new CSI badge, the chief would appreciate it if you left the ballistics lab a cheat sheet about how you worked out who shot Micky.

You can use each technique just once, but some sketches will need more than one to find the missing angle. For a complete list of tool tips in the book, visit www. Angles can be made up of other, smaller angles. Vertical angles are equal and opposite each other. Parallel lines make repeat sets of vertical angles.

F, Z, and N patterns around parallel lines save you a ton of math. In your dreams. Sometimes, size does matter. Bonus gear is up for grabs. Sounds cool! Think you can etch my new cell phone? Meet Liz, your first customer. Liz has picked a design she loves for her new cell phone, now all you have to do is engrave it on the back. What three things do you need to know about each line in order to be able to sketch, and then etch, the design accurately?

What three things do you need to know about each line in order to be able to sketch, and etch, the design accurately?

When you sketch the design, you need to think about these things: He seems to have filled out all the line lengths, but only included a few of the angles?!?

Hand draw the sun and rays 56 40 60 6 48 It certainly looks like there are a lot of angles missing. The design tells us that some triangles are repeated Hand draw the sun and rays 56 40 60 6 48 Same triangle? Yeah, I mean, the designer is talking nonsense. One of them is bigger than the other. How on earth can they be the same?

Well, maybe he was talking about angles. Can you have two triangles with the same angles but with different lengths? Compare your drawings to investigate what happens to the angles of a triangle when you make it bigger or smaller—you just need to make sure that you do the same to each side of your triangle. Does your investigation help you to fill in any of the mystery angles on the design?

Similarity is a key piece of geometry jargon. This means that they have the same equal angles. This F pattern is upside down and back to front! Circle the triangles below that you can be SURE are similar to the triangle repeated in the design. Are they similar? Similarity is maintained even if your shape is reflected or rotated.

We like to think of it as working smarter rather than harder. It does save you plenty of leg work though.

Most geometry teachers will be more impressed by use of similarity than repetitive calculations anyway—just make sure to make a note on your work that you used similarity. Were you surprised? That was incredible. There were so many gaps on that diagram—I never thought we could use those old designs. That must have been a ton of work! How can you tell if two squares or two circles are similar?

Similarity—faster or smarter— which are you? Head First: Do you get a lot of pleasure out of saving people so much work?

It must be nice to be liked. You mean like saving water? I mean like saving brain power! With similarity, you can do a calculation once and then reuse it over and over. Oh, I see! Well, really for me the next step is increasing recognition. Thanks for the quick interview. How will it look? You can We keep spare stock in the store room in case phone from one of these.

What do you think could have gone wrong? The design Liz chose The second mountain is safely intact on the original design. Copy the lengths from the old diagram, but divide them by two. Ask Liz to pick a new design. Start calculating the angles over again. Trash the diagram and go home. Copy the lengths from the old diagram, but multiply them by two.

Do some really hard geometry to work out the new lengths.

A factor is a common multiplier— like if we doubled your pay and also doubled your hours, we would have increased both by a factor of 2. Provided you shrink or grow your shapes proportionally, they can also be similar.

When shapes are proportional, the ratios between the lengths of their different lines are the same. Ratios or angles, which is the real similarity? Go on. You mean you think I can only be one or the other? Well, to be honest, I really am always both! With triangles, and a lot of other shapes, too, if the angles are matching, then the sides are also proportional. Do you feel something is missing?

But that could never happen with a triangle! Anytime triangles have the same ratios, they have the same angles. Ah, well, there are some shapes that are different.

Take rectangles for example. All rectangles have the same angles—90, 90, 90, and 90 degrees. Oh, I do. But only proportional ones. And squares! I love squares. All of them are similar. Every single one. Just beautiful. Beautiful squares, eh?

## Head First 2D Geometry

Thanks for the interview. You can spot similarity using angles or the ratios between lengths or sides, or both. It needs to be half the size of the original. It does look good though! I love it, thanks! Impressed by the effort you put in to getting her phone just right, Liz is trusting you with another great gig. Everyone thinks my phone looks great.

All the arrows are the same. The square part is half the length of the arrow head part. Triangle sides are the same. The sketch is pretty…er…sketchy. Drawn on the back of a flyer by the drummer. Could you use similarity to save yourself some time and effort? We need to find the lengths and angles of the sides of one of the small triangles and one of the big triangles, plus the lengths of the sides of one of the small squares and one of the big squares.

The diagram is made up of six similar arrow shapes like this. This kind of triangle is known as an equilateral triangle the note says the three sides are the same , and all three angles are the same as well. A triangle with three sides all the same length. These three arrows are congruent. How can spotting congruence save you even more time and work than similarity? For starters, congruence means you only have to do one third of the work.

Like the angles between the arrows. You can add parallel or perpendicular lines to your sketch to break down the missing angles into parts you have the tools to find. Adding a line here creates a Z pattern. These two lines are parallel because we say so! Then we can use what we know about these angles… Ready to kick some serious design butt? Use the space on the right to start working on the sketch and calculate them all.

How many of each different angle are there? Feeling overwhelmed? Everything you need is in your Chapter 1 toolbox. Calculate them all. Each arrow head is an equilateral triangle, with 3 equal angles: At the center of the design the darker arrows meet. The tick marks indicate that all the angles with one tick are the same size. To find angle c, draw a line parallel to the base of the dark triangle.

Similarity and Congruence Similarity: You seem neurotic, always concerned about being a size zero, or seven, or whatever. You need to relax more. But size DOES matter. I get used all the time—my flexibility is a real asset. And potentially a real headache! People would do well to use both of us more! Are you getting much non-triangle work these days? Oh, tell me about it! And that we travel so well.

You can flip me upside down, back to front, spin me around and move me from one place to another, and I still work just as well. Great to catch up!

Is there any way you could work up the design so that maybe we could get some t-shirts printed, too? The band would be psyched! Can you really get this diagram to fit perfectly onto all of these without doing a ton of work for each different size?

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But what does that actually mean you need to do? By using ratios rather than actual sizes, you can make your design more flexible. Diagram with correct lengths This is what you need to etch with. The notes the drummer made on the diagram tell you three ratios—what are they? Draw sketches if it helps you figure it out. How come 1: I kinda followed what you did though…with the ratios, and it all makes sense.

You need to take another look. That or the drummer got it wrong. Could it be something to do with it being ratios rather than sizes? What are you going on about? Jim Frank Joe Frank: Yeah, but my dad is four times as old as my kid sister—so, you could say their ages were 4: Relative to what, though?

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On our design, we need to make sure that we reflect all the ratios at the same time, which means we have to pick one thing and then work everything out relative to that. What would be the smallest set of whole numbers you could substitute and still keep the ratios the same? Use your answers from here in this answer.First Edition. Using a scale of 1cm to 1 Kwik-klik unit so a piece of length 2 would be drawn as 2cm , use your ruler to find the part that fits.

NET 4, while avoiding common errors that frustrate many students. Parallel lines can never meet or cross each other, even if you stretch them for miles and miles and miles.

For the four right triangles we tested, it seems like the square of the length of the longest side is equal to the squares of the other two sides added together. Most people can recognize at least one or two of us. Like the angles between the arrows.

Non-integer solutions: Online editions are also available for most titles http: His iPod now rocks our band logo—perfectly etched thanks to some seriously smart number work by the dudes at myPod.

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