Series: Geometry Basics Made Simple

Proofs-Yuk

09/23/2011

~ milly91

I seriously can't do proofs. But this is good and I am getting better at it. I wish you lived next door to me!

Below are the descriptions for each of the lessons included in the series:

• Point, Line, Plane

  Well, this is where you start in Geometry. You're going to learn a lot more about a point, a line, and a plane than you can imagine. Actually it is impossible to "define" these terms so we will just describe them and make sure you know all about them.

  If I can find a "Pointalism" picture from one of my students, I will post it here...just for fun.

  Seriously, all geometric figures are made up of points. We connect points to form shapes of all kinds. So without points, lines, and planes Geometry would not exist.

  Stick with me and you'll be off to a good start!

• Postulates and Theorems

  Even the words sound intimidating! What are Postulates and Theorems anyway? They've been around for a long time and contain all the "rules" of Geometry. This video explains the difference between Postulates and Theorems in a way that is not as strange as they sound.

  Once you know your Postulates, Theorems, and definitions, there is nothing in Geometry that you cannot do. Isn't that a good feeling?

• Midpoint

  Well, now that we've gotten started in Geometry we'll just forge ahead and talk more about points, lines, and planes. What happens when two lines intersect? What does intersect mean? What is a midpoint of a line segment? If two line segments are congruent, what does that mean about the length of each?

  This might be more detail that you really want to know but, just stay with me. In the long run you will be so glad you are comfortable with all these details about distance, length, and congruence.

  Geometry is all about logical thinking. It is about moving from one fact logically to another fact and being able to back them up. You can back up your geometry facts with definitions, Postulates, and Theorems...but you can't make it up and you can't go by "how things look".

  If you agree not to just "go by how things look", that means that we understand everything must have a valid reason.

• Introduction To Angles

  You hear people talking about angles all the time but what, exactly, are they? I know it sounds like a simple questions, and it is really, but looking closely at the definition will start you off with a firm footing in Geometry. Math help isn't really very helpful if it skips too much material and starts you off in the dark!

  This video will define "angle" for you and show you exactly what an angle is and what makes an angle. Then it will talk with you about different kinds of angles so when you come across these terms, you will know what they are talking about.

  For example, if I go on and on about adjacent angles, and you have no idea what that means...it really doesn't matter what else I say because you will be lost. That's what happens in many classrooms. Always ask when there is something you don't understand.

  However, there is only so much time in a "regular" classoom so it's impossible for your teacher to stay on the basics for very long. Me? I can stay on them as long as I want to. And you can replay me as many times as it takes.

• More About Angles

  When you listen to your teacher in Geometry,she, or he, will mention angles every day about a hundred times! You see, then, how important they are. If you don't want to get lost, stick with this video until you really understand all of it.

  The Angle Addition Postulates is explained on this math help video. There are a lot of times you need to add angles together. It might seem kind of obvious but it is necessary to learn how to add them, how to name them, and what allows you to add them. That's where the Angle Addition Postulate comes in. Your book might call it something else similar.

  Some pairs of angles are called complementary. Some pairs are called supplementary. And some pairs are called Linear Pairs. Whew! That's a lot of different pairs of angles. Not hard though. You'll see.

  Watch the video whenever you need to review these terms and again right before the test.

• Bisectors and Vertical Angles

  As you study Geometry you will become best friends with bisectors and vertical angles! This video makes sure you know what they are and how to recognize them. I will first define them for you and then show you many examples. Once you see what they are and how they work, geometry math problems will be so much easier for you to do. Some will seem "flat out" easy!

  Algebra examples are included in this geometry video lesson. They are great practice. You will surely have these type problems in your class at school. Watch me work them, then work them on your own until you totally "get it".

  This video introduces you to vertical angles. It makes sure you know what vertical angles are. It teaches you that vertical angles are formed whenever two lines cross.

  Bisectors of segments and angles are found throughout Geometry. This lesson helps you know what both kinds of bisectors are....for sure, before you start using them in theorems and postulates.

  If you need a good foundational video to begin your study of geometry, this is one that is essential.

• Bisectors and Vertical Angles

  Before you can start working problems with bisectors and vertical angles you have to know what they are. My teaching methods help you learn by seeing and hearing the information. I use a lot of repetition and drawings to help you learn.

  This video introduces you to vertical angles. It makes sure you know what vertical angles are. It teaches you that vertical angles are formed when two lines cross.

  Bisectors of segments and angles are found throughout Geometry. This lesson helps you know what a bisector is....for sure, before you start using them in theorems and postulates.

  If you need a good foundational video to begin your study of geometry, this one is essential.

• How To Prove Vertical Angles Are Congruent

  Vertical angles! We love them! They are so easy to use and provide a real comfort level when beginning Geometry. This proof shows you "why" vertical angles are congruent. It proves that they are 'always' congruent. If you need to see how and why vertical angles are congruent, watch this.

  Once this theorem is proven, it can be used anytime in the future when you have vertical angles. First of all make sure you recognize vertical angles so you will know when you have them. Then be on the look out for them!

  Vertical angles are formed whenever two lines cross (intersect). You will find them hidden in many drawings that contain more than two lines. That is why you want to look for them. Think of it as a puzzle and keep your eyes open for vertical angles.

  After this video you will understand why they are always congruent and you will understand how to work with them. Whenever you get a problem with vertical angles, go ahead and mark them congruent as soon as you sketch the drawing. Don't draw too small. The more you can actually see, the better and quicker solutions will begin to come together.

  Enjoy working with vertical angles. They usually lead you to more information to help you solve a problem.

• If-Then Statements

  Geometry is just full of If-Then Statements! Usually they are called Conditional Statements. We all use if-then statements everyday as we go about our day. This video will help you see what conditional statements are actually saying to you...in Geometry.

  Converse statements, Inverse statements, and Contrapositive statements all start with a Conditional statement. What ARE all those kinds of statements? This video will tell you. That way, when you see it on your SAT, you will know exactly what it is talking about. Gotta speak the language to have any shot at success.

  We will see what happens to a statement when we swith the if-then parts, or if we make them both negative.

  You probably know "hypothesis" and "conclusion" from Science. That will help too.

• Parallel Lines And Angles

  Parallel lines are everywhere you look in Geometry. They are found in squares, rectangles, and parallelograms. The information you gain through parallel lines is mostly about angles so this video will focus on angles formed by parallels.

  Students like this section because there are patterns which are easy to see. Once you see the patterns and learn the names of the angles you can work almost any problem with parallel lines.

  Just remember. Whenever you see lines that are parallel, it is all about the angles formed by the transversal. Look for them!

• Examples With Parallel Lines and Triangles

  Parallel lines form many angles when cut by another line called a transversal. You can imagine how many angles are formed when you have more than one transversal! All those angles have names, thank goodness, so we can keep them straight! Such pairs are the alternate interior angles, corresponding angles, and same side interior angles. And what about the converses of these postulates?

  In this video you will learn all these angles and more. You will see how they show up in triangle problems. Once you learn all the names and how they work, you'll be looking everywhere for parallel lines because you'll find them easy problems to work.

  Geometry will, sooner or later, start fitting together like a big jigsaw puzzle. It is not very enjoyable until that happens. As long as it makes no sense it will be a dreaded subject. But once you begin to see how it all fits together, you will begin to like it...a lot!

  Watch, work the problems, watch again as many times as you need. Master this material and you'll be on your way to smoother sailing!

• Parallel And Perpendicular Lines - Proofs

  This video proves two theorems.

  1. If two lines are perpendicular to the same line, then they are parallel.
  2. If two lines are parallel to the same line, then they are parallel.

  Follow along with me as I prove these two concepts. We certainly don't have time to prove every theorem but these two are proven here. They are not necessarily the most important but they may help you learn how proofs work.

  After you work through them with me, turn off the screen and try it by yourself. Copy the 'given' and the drawing before you turn off the screen.

  Even if the proof itself is confusing, and even if you can't prove it by yourself, it's okay for now. The important thing right now is to be able to understand how each step flows logically from the previous step.

  "How To Write A Proof" will come later. :)

• Kinds Of Triangles

  Triangles are one of the most familiar shapes in the world. As simple as a triangle is, there are several different kinds of triangles and they have different properties. We will also look at the interior, the exterior, as well as the triangle itself.

  In this video you will learn all about each type of triangle. You will learn about their angles and their sides and the relationships between sides and angles. Make sure you commit all definitions to memory so when you need to write a proof involving a triangle, you will have all the tools you need.

  Enjoy this lesson. It's very straightforward and not difficult at all. Just get all the details and terminology! Success is in the details!

• 180 Degrees In A Triangle

  In this video you will learn two very important theorems about triangles. Not only will you learn the theorems but you will see me prove them. As I walk you through the proofs you will become more comfortable with writing your own proofs in the future. Right now just focus on learning these two concepts.

  Ever wondered why there were 180 degrees in every triangle? No matter the size, type, or location of a triangle, the angles always add up to 180 degrees. This video will show you why. This is a theorem you must, must, must learn. Or else....as they say!

  Another theorem on this video is the Exterior Angle Theorem. I am proving this theorem for you by writing a formal proof. Watch me, listen carefully, follow the steps. It is intended only to help you get more comfortable with proofs.

  The more comfortable you get, the less you will freak out when you have to write a proof of your own. It's coming you know. Better to get all these basics out of the way first!

  Work hard!

• 3rd Angle Of A Triangle Proof

  It's fairly obvious that if two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. However, how to write the proof may not be so obvious. For that matter, how to write ANY proof may not be so obvious!

  That is probably the understatement of the world! Most students find proofs to be very difficult. This video "illustrates" a proof but doesn't really teach you how to write a proof. That will need a video all it's own! Coming soon.

  For now, the most important part of this video is to get the concept of the 3rd angle...and, thank goodness, that IS very easy to get.

  Learn this theorem. Do not worry if you cannot write the proof as I did. Try to follow me though. At this stage, being able to just follow my proof is enough. The concept is important to know. The proof...just follow me for now.

• Properties Used In Proofs

  Many students have trouble writing proofs by themselves. One essential step when writing Geometry proofs is knowing the definitions, properties, and theorems. This video explains the most used properties.

  Whether in Geometry or Algebra, for example, the Addition Property of Equality is used over and over.
  Very simply put, you use this property whenever you add the same value to both sides of an equaition.

  In this video you will see examples of this property plus the Subtraction Property of Equality, Multiplication Property of Equality, and Division Property of Equality.

  Other properties that occur frequently are the Reflexive Property, Symmetric Property, and Transitive Property.

  Watch the video. Refer back to it as often as you need to until these properties are as easy as pie and as clear as day!

• Using Algebra To Find Angle Measures

  Did you like Algebra? I hope so, because, many times in Geometry you are asked to solve for x. So if you thought you could get away from Algebra, oops, you were wrong! If you liked Algebra you are probably cheering to get back where you are comfortable.

  You must also know your geometry definitions to know how to set up your algebra equation. Solving the equation is almost always easy...once it is set up. The hard part comes when you are trying to set it up! The more definitions (in Geometry) that you really understand, the easier it is to set up your equation. Watch me and you'll see what I mean.

  In this video I will work problems with angle bisectors that form angles with equal measures. Also we'll work with linear pairs and supplementary angles.

• Commutative, Associative, Distributive, Identity

  This video explains the Commutative, Associative, and Distributive Properties. They are not very fun or interesting,to tell you the truth, but you need to know them. When I first learned them I thought they were pointless. I didn't understand why in the world they were in every math course I took. You may be like that too. Eventually, as you take more and more math classes, you will see that they never go away...and you'll begin to understand why you need these properties. This video lesson is more like eating your veggies than eating dessert! Just telling you the truth.

• Algebraic Examples In Geometry

  Sometimes you just need extra practice in solving geometry problems using algebra. Most students like this part of Geometry more than proofs and definitons. Do you?

  You have four problems to solve on this video. Work them along with me. One is vertical angles. One uses angle bisector. A third problem uses linear pairs and the last problem uses supplementary angles.

  First of all, solve for x. Then find the measure of the angle. It is so easy to double check these and know for sure if you are right. I think you'll like these.

  As I say in the videa "Math is not a spectator sport." You can't just watch and just listen if you want to really learn and remember what you learn. You have to do the problems too. Work them with me, then work them by yourself.

Supplementary Files:

• Once you purchase this series you will have access to these files: