TabletClass Math Geometry Course Guidebook

Transcription

1 TabletClass Math Geometry Course Guidebook Includes Final Exam/Key, Course Grade Calculation Worksheet and Course Certificate Student Name Parent Name School Name Date Started Course Date Completed Course Final Grade Copyright 2014 TabletClass.com, LLC

2 Table of Contents Introduction and Special Message From Teacher... 3 Chapter Tests Summary Worksheet... 4 Course Guidebook... 5 Final Exam Directions Final Exam Final Exam Key Course Grade Calculation Worksheet Course Pacing Guidelines Course Certificate Copyright 2014 TabletClass.com, LLC 2

3 Introduction Special Message from the Teacher: Welcome to the TabletClass Math Geometry course. First I want to say that I m very excited to have you as a student. My goal is to give you an enjoyable and high quality learning experience. Moreover I want you to know that you can master this material if you work hard and never give up. This guidebook and final exam is an important part of the course so I strongly recommend that you use the included material. The secret to being successful in mathematics is your approach to studying the topic- i.e. your study habits. From years of teaching math I can say that those students with the best study habits almost always earn the top grades. As such parents and teachers must focus on holding students accountable for the quality of their work. Below are critical guidelines for students as they take the course: 1. Never give up- especially when a topic is not understood easily or immediately 2. Strive to be as neat and organized as possible 3. Excellent note taking is a must to succeed in math 4. Show all steps when working problems 5. Double check your work as you write your solution steps 6. Always go back and review incorrect problems and discover where the error was made 7. Master the fundamentals and don t move forward unless you understand previous material Suggested use of the follow along guidebook and final exam: 1. Maintain the guidebook as a written record of the online TabletClass Math student s account 2. The guidebook and final are designed to be a part of the student s overall course portfolio 3. Carefully read the final exam directions before giving the final to student 4. Use the course grade worksheet as input for the final grade assigned Remember the course material builds on itself so you want to ensure that you don t skip chapters and sections. Furthermore you want to correct your weak areas before moving onto the next topic. The guidebook and online self-assessment / my pulse software features will help you manage your progress. Lastly, I want to stress that you can be great in math if you work hard. Even if you have struggled in math before I want you to look at this course as a fresh start in your mathematics journey- I know in my heart you can ace this course! Best of luck! John Zimmerman TabletClass Math Teacher Copyright 2014 TabletClass.com, LLC 3

4 Geometry Chapter Tests Summary Chapter 1: Foundations for Geometry Chapter Test Score Date Taken Chapter 2: Reasoning and Proof Chapter Test Score Date Taken Chapter 3: Perpendicular and Parallel Lines, Polygons Chapter Test Score Date Taken Chapter 4: Congruent Triangles Chapter Test Score Date Taken Chapter 5: Properties of Triangles Chapter Test Score Date Taken Chapter 6: Quadrilaterals Chapter Test Score Date Taken Chapter 7: Similarity Chapter Test Score Date Taken Chapter 8: Transformations Chapter Test Score Date Taken Chapter 9: Right Triangles and Trigonometry Chapter Test Score Date Taken Chapter 10: Circles Chapter Test Score Date Taken Chapter 11: Area and Volume Chapter Test Score Date Taken Copyright 2014 TabletClass.com, LLC 4

5 TabletClass Math Geometry Course Follow Along Guidebook Chapter 1 Chapter 1: Foundations for Geometry This chapter will introduce students to the key terms and concepts in geometry. Students will learn how to write the notation for various geometric expressions like angles, lines, rays, planes, points and segments. Lastly, the concept of theorems and postulates are introduced and their importance explained. Section Summary (circle / complete after chapter is finished): 1. Welcome to Geometry 2. Points, Lines and Planes 3. Line Segments, Rays 4. Angles 5. Theorems and Postulates Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 5

6 Ch. 1 Section 1 Welcome to Geometry This section is a quick introduction to the topic of geometry. The video will discuss some of the topics students will see through the course. No specific lesson is taught. Ch. 1 Section 2 Points, Lines and Planes In this section I will introduce you to the building blocks of geometry- points, lines and planes. Hence, it s important that you understand how we define and think of these concepts. Geometry is very different than algebra so you will be learning an entirely new mathematical language. As such you need to take excellent and organized notes because I will be teaching you a lot of new symbols, notations and theorems. In this lesson my goal is to get you to understand how points, lines and planes relate. Now this may sound strange but points, lines and planes cannot be defined in geometry- I will explain why in the video. I m sure you have a good sense of what a point is or a line is but as you will see in the lesson these terms cannot be strictly defined. However we still can learn a lot about the properties of points, lines and planes and apply this knowledge to the wonderful world of geometry. Welcome to course I know you will learn a lot! Example Set C Copyright 2014 TabletClass.com, LLC 6

7 Ch. 1 Section 3 Line Segments, Rays In this section I will teach you about line segments and rays. A line segment is basically what the name implies- it s just a piece of a line with end points. Along with the definition of a line segment you need to understand the proper notation to describe a line segment. The next shape we will look at is the ray. You can think of a ray like an arrow in the sense it has one starting point and travels out in specific direction. The key difference between a line segment and ray is that the line segment has two end points where as the ray only has one. The notation for a line segment and ray are similar so be careful not to confuse the two. Like I said in the previous lesson, geometry has lots of symbols and notations so you need to watch the details of these symbols as many will look similar. Ch. 1 Section 4 Angles In this section I will teach you about angles. As you can imagine angles have a huge role to play in geometry so we need to know them well. First, let s start with a basic definition of an angle; an angle is simply two rays that start from the same point called a vertex. Like all new shapes we learn in geometry we will need to master the symbols and notation associated with angles. Now that you have a good sense of what an angle is we can explore the various types of angles. In the lesson I will classify different angles to include right, acute and obtuse angles. Also we will explore a few key properties that angles contain. As our knowledge of geometry builds you will learn much more about angles especially when they are formed in triangles or intersecting lines. Stay excited as you will see how geometry will relate to real life shapes and situations. One last thing- make sure to review your notes frequently to ensure you are retaining the material. Example Set C Copyright 2014 TabletClass.com, LLC 7

8 Ch. 1 Section 5 Theorems and Postulates In this section I will introduce you to theorems and postulates. By the time you finish geometry you will have learned and studied many, many, many theorems and postulates. So let me give you a quick definition on them- let s start with postulates first. A postulate is a mathematical law that we can t prove but we accept on faith. For example the idea that two parallel lines never cross is a postulate- we accept this as fact but in mathematics we actually can t prove this. You may be thinking that you can prove two parallel lines never intersect but if you put your arguments into a mathematical proof you would not be able to prove it. Many famous mathematicians have tried and failed to come up with a parallel line proof for hundreds and hundreds of years- so if you can prove it great! However just because we can t absolutely prove that parallel lines will never intersect we can believe it anyway and turn our belief into a mathematical law. Now that you have a sense of what a postulate is we can now define a theorem. A theorem is simply a mathematical property or law that we can prove using postulates and logic. Let s take a look at the lesson so you can start learning your first postulates and theorems in geometry. Copyright 2014 TabletClass.com, LLC 8

9 Chapter 2: Reasoning and Proof TabletClass Math Geometry Course Follow Along Guidebook Chapter 2 In this chapter students will study the role of logic and proof in geometry. Students will learn how to identify the hypothesis and conclusion in conditional statements and write the converse. In addition, students will learn more about the properties of lines and angles. Lastly, students will learn the structure of a geometric proof and study the steps to write an entire proof on their own. Section Summary (circle / complete after chapter is finished): 1. Conditional Statements and Converses 2. Algebra Properties 3. Deductive and Inductive Reasoning 4. More on Angles and Lines 5. How to Plan and Write a Proof Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 9

10 Ch. 2 Section 1 Conditional Statements and Converses In this section I will teach you about conditional and converse statements. We need to study this because part of what we do in geometry is write proofs. A proof is a way of proving something using logic, properties, theorems and postulates. Confused? Don t worry I will explain proofs in details in this and future lessons. If you ask anyone that has taken high school level geometry they may not have great memories of doing proofs because they can be challenging and confusing. Hence you really want to focus on this lesson and take excellent notes. So let s do a quick introduction to conditional and converse statements. A conditional statement is nothing more than an if-then statement. For example the statement if it rains I will then need my umbrella is a conditional statement. The converse is a statement where we flip a conditional statement around- let s use the above statement to find the converse- if I need my umbrella then it s raining. Do you see the connection between the two statements? No worries my lesson will make these concepts clear- good luck! Example Set C Ch. 2 Section 2 Algebra Properties In this section I will teach you about the properties of algebra. Now you might be wondering why we are studying algebra in geometry but as the course goes on you will see how much we use algebra to solve geometry problems. So let me take this time to encourage you to review your algebra skills frequently so they remain sharp not only for geometry but for future math courses like algebra 2. Ok so what are algebra properties and why do we need them in geometry? First let s start with examples of an algebra property. Do you remember the distributive property? If you do, then you remember a very important algebra property. The property helps us simplify problems like 3(x + 2) and write it in an equivalent form of 3x + 6. We were able to do this because the property states we can distribute or multiply the 3 to the x and 2. Algebra properties are laws that we need to follow in algebra. However these same algebraic properties have a geometric equivalent and we will need to know these properties to write proofs- FUN! Like always take good notes and practice as much as you can. Example Set C Copyright 2014 TabletClass.com, LLC 10

11 Ch. 2 Section 3 Deductive and Inductive Reasoning In this section I will be teaching you about deductive and inductive reasoning. As you know we do a good amount of proofs in geometry. A proof is a structured, organized way to argue our belief. For example if I said prove a pencil is not a pen. Well you might start this proof by saying ok can we agree that a pencil uses lead and a pen uses ink? Then you might say because the definition of a pencil is only those writing instruments that use lead I conclude a pen is not a pencil. Now this might seem like a silly example but the point I m trying to make is how I organized and walked a person through my argument. This organized way of arguing is called logic and that s what we will be studying. As you will see in the lesson there are two types of logic- deductive logic and inductive logic. You need to know them both but we will be using deductive logic the most in geometry. Enjoy the lesson and take good notes. Ch. 2 Section 4 More on Angles and Lines In this section I will be teaching you more about angles and lines. I can t stress how important it is for you to master and understand all the various properties about angles and lines as we will be using them a lot in geometry. Some of the things we will be studying in the lesson are complementary and supplementary angles as well as vertical angles. Complementary and supplementary angles are those angles that are formed with respect to 90 and 180 degree lines- you will see this clearly in the lesson. Vertical angles are those angles formed when two lines intersect. Like I was saying the building blocks of geometry are angles and lines- so as you can imagine there is a lot of properties, theorems and postulates to learn. Please take excellent notes and practice is a must if you really want to master the concepts. Example Set C Copyright 2014 TabletClass.com, LLC 11

12 Ch. 2 Section 5 How to Plan and Write a Proof In this section I will teach you how to plan and write a proof. This will be an extremely important lesson as most students struggle doing proofs at first. The key to becoming proficient at doing proofs is practice- it s as simple as that. However I made this lesson to give you a head start and structure your approach to geometric proofs. One of the biggest things you want to take away from this lesson is the allowable reasons you can use in a proof. What I mean is any statement you write in your proof needs to be justified- this is the essence of deductive logic. You will see in the lesson there are 5 types of reasons you can use to justify your statements. Some of these reasons include postulates, theorems and properties. Hence you need to have excellent organized notes on all the theorems, postulates and properties we have learned (and will learn) as you will need them for your proofs. Lastly you will learn how to properly write a two column proof- one column will be statements and the other column will be reasons. Example Set C TabletClass Math Geometry Course Copyright 2014 TabletClass.com, LLC 12

13 Follow Along Guidebook Chapter 3 Chapter 3: Perpendicular and Parallel Lines, Polygons In this chapter students will study the relationships of perpendicular and parallel lines. Several important properties will be covered that are essential to solve common problems in geometry. A critical section in this chapter is dedicated to theorems that state when two or more lines are parallel. Students are also introduced to polygons and their types. Section Summary (circle / complete after chapter is finished): 1. Parallel Lines and Transversals 2. Properties of Parallel and Perpendicular Lines 3. Proving Lines Parallel 4. Introduction to Polygons Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 13

14 Ch. 3 Section 1 Parallel Lines and Transversals In this section I will teach you about parallel lines and transversals. Everything we learn in geometry is important but this lesson is extra important because we will be using so many of the concepts in this lesson to learn future material. I m pretty sure you have a good idea what parallel lines are so let s talk about what happens when we chop two parallel lines with another line. A line that chops or intersects two or more parallel lines is called a transversal. The angles formed (which there are many) by the parallel lines and a transversal is what we will be focusing on in this lesson. As such be prepared to write down many important theorems and postulates that describe what happens with all these angle relationships. Lastly are you reviewing your notes on previous material? You should be consistently reviewing your geometry notes because the course builds on itself. One suggestion to help you study is high lighting all the theorems and postulates in your notes so you can quickly identify them. Example Set C Ch. 3 Section 2 Properties of Parallel and Perpendicular Lines In this section I will be teaching you about the properties of parallel and perpendicular lines. A word of warning: there will be lots of theorems and postulates in the lesson so be ready to take good notes. In the lesson I will continue to build your knowledge of parallel lines and introduce you to perpendicular lines. You may know that perpendicular lines are those lines that are formed when two lines meet at right angles- i.e. the angle formed is 90 degrees. As I will show you in the lesson there are some pretty cool features about perpendicular lines that you need to know. I want to continue to stress that in geometry we do proofs and you will be expected to recall all previous theorems, postulates and properties. Now I don t expect you to know them by memory but you should be able to quickly reference them in your notes. As such if your notes are not well organized, complete and neat I would recommend you take the time to rewrite them properly. Once you complete geometry you re notes can become a wonderful reference for you to review for tests like the SAT/ACT so be smart and invest in developing your note taking skills. Example Set C Copyright 2014 TabletClass.com, LLC 14

15 Ch. 3 Section 3 Proving Lines Parallel In this section I will teach you how to prove if two or more lines are parallel. Now I want to be very clear that we will focus on proving lines parallel- not if two parallel lines intersect. If you recall in my lesson on theorems and postulates I used the fact the mathematicians have not been able to prove two parallel lines intersect- however we assume that they don t and we express this concept as a postulate. All we are doing in this lesson is looking at the relationship between two lines and seeing if conditions exist such that we can prove the lines are parallel. Make sure you watched all the previous lessons in this chapter as we will use the properties and theorems in those lessons in our proofs. Now if you re feeling overwhelmed by all this take a step back and review and of course watch the videos as much as you like. Remember we are studying pretty abstract concepts and so give yourself time to fully comprehend new skills and knowledge. Example Set C Ch. 3 Section 4 Introduction to Polygons In this section I will introduce you to polygons. You may already have a good idea what a polygon is so let s build upon what you already may know. A polygon is a closed figure that has multiple sides that are line segments. The first polygon you know is the triangle- it has 3 sides and the figure is closed. Can you think what we call a 4 sided polygon? Yes you are correct it s called a quadrilateral. However we have all different types of quadrilaterals to include squares, rectangles and rhombuses. As you can imagine our study of polygons will be vast and central to the topic of geometry. Please take great notes as you will be learning a lot of theorems, postulates and properties about various polygons. In later chapters we will investigate the details of two specific polygons- triangles and quadrilaterals. Enjoy the lesson and keep working hard! Example Set C Example Set D Copyright 2014 TabletClass.com, LLC 15

16 TabletClass Math Geometry Course Follow Along Guidebook Chapter 4 Chapter 4: Congruent Triangles Congruency is a core concept in geometry. Students will learn the concept of congruency by studying the properties of congruent triangles. After an introduction to congruent figures students will focus on learning to prove triangles are congruent using the SSS, SAS, ASA, AAS and HL Theorems. Section Summary (circle / complete after chapter is finished): 1. Congruent Figures 2. Proving Congruent Triangles: Side-Side-Side and Side-Angle-Side Theorem 3. Proving Congruent Triangles: Angle-Side-Angle and Angle-Angle-Side Theorem 4. Proving Congruent Triangles: Hypotenuse-Leg Theorem Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 16

17 Ch. 4 Section 1 Congruent Figures In this section I will teach you about congruent figures. The concept of congruence is extremely important in geometry and we will focus our attention on it in this chapter. When two figures have the exact same shape and size we describe them as being congruent. For example exact copies of a toy car would be congruent because they have the same shape and size. There is a concept in geometry for figures that have the same shape but a different size- we call this concept similarity and we will be studying it as well. One of the most important concepts you will learn in the lesson is corresponding parts of congruent figures are congruent- much more about this in the video. Lastly this lesson will be the foundation of many important triangle theorems that you must master so take excellent notes! Ch. 4 Section 2 Proving Congruent Triangles: Side-Side-Side and Side-Angle-Side Theorem In this section I will teach how to prove two triangles congruent by the SSS and SAS theorems. The SSS theorem stands for Side-Side-Side and the SAS theorem stands for Side-Angle-Side. Now the sides and angles we are talking about are those of two triangles we are trying to prove congruent. Hence if two triangles have the exact side lengths (all sides) then we can use the SSS theorem to conclude they are congruent. Likewise if two triangles have two sides and an angle that are the same measure we can use the SAS to prove them congruent. In this lesson we are focusing on proving so we will be doing proofs. As such you may want to review your notes on how to plan and write a proof or watch the video lesson on this topic over again. Copyright 2014 TabletClass.com, LLC 17

18 Ch. 4 Section 3 Proving Congruent Triangles: Angle-Side-Angle and Angle-Angle-Side Theorem In this section I will teach you the ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) theorems for proving triangles congruent. The ASA theorem states that two triangles are congruent if there is a corresponding angle, side and angle measures that are equal. Likewise the AAS theorem states two triangles are congruent if they have an equal corresponding angle, angle and side measure. Of course the video will demonstrate the theorems more clearly so you need to watch the lesson to fully master the concepts. Keep in mind that most of theorems in this chapter have to do with proving two triangles congruent. As such the key skill you need to master about these theorems is writing proofs. As I stated in previous lessons you need to really work hard on proof writing- it s not easy. Math is about problem solving and critical thinking and writing proofs is an excellent way to develop these important aptitudes. Ch. 4 Section 4 Proving Congruent Triangles: Hypotenuse-Leg Theorem In this section I will teach you the Hypotenuse-Leg theorem for proving triangles congruent. This is a nice special case theorem for congruent triangles. As the name implies we can prove two triangles congruent if they have hypotenuses (longest leg of a triangle) and another corresponding side congruent. Now what makes the HL theorem a special case theorem is it only applies to triangles that are RIGHT- i.e. one of the angles is 90 degrees. Assuming you have watched all the other lessons in this chapter you know we have many theorems to prove triangles congruent. Just a quick review these theorems are the SSS, SAS, ASA, AAS and now finally the HL theorem. Don t think anyone method or theorem is better than another. You need to master all the congruent triangle theorems as it will give you more problem solving tools in geometry. Please continue to focus on taking well organized notes and practice is a must. Quick question: could you easily identify all the postulates and theorems you have learned in the course so far? If not be smart and get your notes organized the effort will pay off. TabletClass Math Geometry Course Copyright 2014 TabletClass.com, LLC 18

19 Chapter 5: Properties of Triangles Follow Along Guidebook Chapter 5 In this chapter students will learn the various properties of triangles. Several definitions and theorems will be introduced about the medians, altitudes and bisectors of triangles. In addition the chapter has an important section on the inequalities found in triangles between sides and angles. Section Summary (circle / complete after chapter is finished): 1. Medians, Altitudes and Bisectors 2. Bisector Theorems 3. Triangle Inequalities Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 19

20 Ch. 5 Section 1 Medians, Altitudes and Bisectors In this section I will teach you about medians, altitudes and bisectors. All of these topics are a detailed look into triangles. As I will show you in the lesson triangles have some very interesting properties of which you need to master. One of the skills that you want to focus on in this lesson is the construction of a figure. What I mean by the word construction is your ability to draw an accurate sketch that shows medians, altitudes and bisectors. I would suggest that you have a compass, protractor and ruler to help you with your drawings. Measuring and drawing triangle properties on paper will make you understand the theorems much better- it s also a great learning experience. However before you can construct these figures you need to have a clear definition what medians, altitudes and bisectors are. Make sure you taking excellent notes as these terms have exact definitions that you need to fully comprehend. Ch. 5 Section 2 Bisector Theorems In this section I will be teaching you about bisector theorems. As I suggested in the previous lesson you really want to make constructions of these triangle theorems as it s a great way to experience the concepts in real life. My lesson will explore angle and perpendicular bisectors theorems. Just as the name implies an angle bisector is a ray that bisects or cuts an angle measure in half. For example, the angle bisectors of a 60 degree angle would cut and form two 30 degree angles- you will see this clearly demonstrated in the lesson. Now a perpendicular bisector cuts a line segment in half. The key concept about a perpendicular bisector is that it bisects another line perpendicularly meaning at a right angle (90 degrees). If you re a little confused don t worry the video will show this much more clearly. As I was saying, don t forget to create constructions on the theorems and properties we cover- it s a great way to understand and retain the concepts. Lastly keep reviewing your notes as geometry builds on itself. Have you done any algebra problems lately? You should- remember there is algebra and geometry and you should be reviewing algebra as well. Copyright 2014 TabletClass.com, LLC 20

21 Ch. 5 Section 3 Triangle Inequalities In this section I will teach you about triangle inequalities. I find the triangle inequality theorems to be very interesting and of course I hope you do as well. Basically, triangle inequalities look at the relationship between angles and sides of triangles. There is a triangle inequality theorem that relates the measure of all the angles in a triangle and another theorem that relates the sides of a triangle. Now I won t give too much away about the theorems before the video however I will say that you definitely want to practice this topic. I have seen more than a few SAT/ACT problems that relate to the triangle inequalities so make sure you learn them well. The good news is the theorems are pretty straight forward and easy to understand. Nevertheless the only way you will be able to master the concepts is by practicing. Question: are you using pen or pencil when doing math? Please use pencil it s just a much easier way of keeping your work neat. Good luck and enjoy the video. Example Set C Copyright 2014 TabletClass.com, LLC 21

22 TabletClass Math Geometry Course Follow Along Guidebook Chapter 6 Chapter 6: Quadrilaterals In this chapter students will learn the various properties and type of quadrilaterals. The first two sections focus on the properties of parallelograms to include proving a quadrilateral is a parallelogram. Next additional sections look in-depth at trapezoids, special quadrilaterals to include the rhombus and theorems involving midpoints in quadrilaterals and triangles. Section Summary (circle / complete after chapter is finished): 1. Parallelograms 2. Proving Quadrilaterals are Parallelograms 3. Trapezoids 4. Special Quadrilaterals 5. Quadrilaterals, Triangles and Midpoints Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 22

23 Ch. 6 Section 1 Parallelograms In this section I will teach you about parallelograms. As we study this chapter we will focus on various types of quadrilaterals and one of the most common types of quadrilaterals is the parallelogram. Most students have a good idea on what a parallelogram looks like. However, I would imagine that many students would struggle to give an exact definition of what a parallelogram is- could you define a parallelogram exactly? Of course if you don t really remember what a parallelogram is don t worry I will cover lots of details about parallelograms in the lesson. Also make sure you are ready to take notes as I will be giving you many theorems on the sides, angles and diagonals of a parallelogram. Like I was saying we will be studying many different types of quadrilaterals in this chapter and the material builds on itself so be prepared. Ch. 6 Section 2 Proving Quadrilaterals are Parallelograms In this section I will teach you how to prove a quadrilateral is a parallelogram. Not every quadrilateral is a parallelogram so it s important to for you to know how to identify and prove when a quadrilateral is in fact a parallelogram. Now why would you care if a quadrilateral is or is not a parallelogram? Well one good reason is that once we know a figure is a parallelogram we know a lot about it s properties and this information can really help us solve problems. Hence you want to know methods of proving a quadrilateral is a parallelogram and that s our focus in this lesson. As you will see in the video we will be using lots of theorems to prove a quadrilateral is a parallelogram. The basic idea is you will look at a quadrilateral and see if it matches the properties of a parallelogram- if it does than you can prove the quadrilateral to be a parallelogram. Don t forget the lessons on how to plan and write a proof as it will help you a lot with this topic. Example Set C Copyright 2014 TabletClass.com, LLC 23

24 Ch. 6 Section 3 Trapezoids In this section I will teach you about trapezoids. A trapezoid is a special type of quadrilateral. Just like a parallelogram is a special quadrilateral so is the trapezoid. This lesson will focus entirely what makes a trapezoid unique. As you will see in the video the trapezoid is a little more complex than a parallelogram. Hence you want to take your time with the lesson so you understand the parts and terms related to a trapezoid. It s easy for a student to get all the various quadrilateral theorems and properties confused so make sure your notes are well organized and clear. Quick pop quiz: do you know the difference between a parallelogram and a trapezoid? Well if you said a trapezoid only has one pair of parallel sides where a parallelogram has both pairs of opposite sides parallel you would be correct. Also, the area formulas for a parallelogram and trapezoid are much different. Like I was saying trapezoids have more aspects than parallelograms so pay attention to the details. Don t forget to keep reviewing algebra- you will see algebra used in many geometry problems so keep your skills sharp. Ch. 6 Section 4 Special Quadrilaterals In this section I will teach you about special quadrilaterals. If you have been watching the lessons in this chapter in order you know that we have explored parallelograms and trapezoids- both very common types of quadrilaterals. In this lesson we will look at other special quadrilaterals to include the rectangle, square and something called a rhombus. All the figures I just mentioned are a part of the quadrilateral family and quadrilaterals are a type of polygon- confused? Well it can be confusing if you re not taking great notes and reviewing previous lessons. In geometry there are so many theorems, postulates, definitions and properties that seem similar but in fact they are not- it s easy for anyone to mix concepts up so be careful. The way to successfully master all the material is by taking neat and organized notes and then practice, practice, practice. Remember, you will see geometry again especially if you plan on going to college as the SAT/ACT tests are filled with geometry questions. Keep working hard and never give up! Example Set C Copyright 2014 TabletClass.com, LLC 24

25 Ch. 6 Section 5 Quadrilaterals, Triangles and Midpoints In this section I will teach you more about quadrilaterals, triangles and there midpoints. As you can tell there is a lot of information you need to learn about quadrilaterals and triangles and each theorem and property is important. Hence you need to remain focused on all the details I explain in the video and ensure you are taking great notes. One of the things I will talk about in the lesson is what happens when a transversal (a line) intersects parallel lines- especially if the transversal is cut into congruent segments. Also, I will get into what a midpoint of a triangle is and the relationship it forms with the sides of a triangle. If you have been going through the lessons in this course in order you already have increased your knowledge of triangles significantly. Additionally you know a lot of powerful theorems about parallel lines and various quadrilaterals. But as you will see in future lessons we have a lot more to learn about these and other topics so stay excited and practice as much as you can. Example Set C Copyright 2014 TabletClass.com, LLC 25

26 TabletClass Math Geometry Course Follow Along Guidebook Chapter 7 Chapter 7: Similarity Similarity is a core geometric relationship. To solve most similar polygon problems students need to have the algebra skills to solve ratios and proportions, hence this is the first section in the chapter. The remaining sections focus on similar polygon problem solving and the properties and theorems of similar triangles. Section Summary (circle / complete after chapter is finished): 1. Ratios and Proportions 2. Similar Polygons 3. Similar Triangles Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 26

27 Ch. 7 Section 1 Ratios and Proportions In this section I will teach you about ratios and proportions. Because you did great in algebra you should already be a master at ratios and proportions- but if you re a little unsure don t worry I will review the topic completely. Let s remember that ratios and rates are just fractions. What makes them unique is that ratios and rates are fractions that use numbers with units of measure. Example 1/3 is a fraction however 1 teacher / 3 students is a ratio. Now a proportion is an equation of two equal ratios or rates- i.e. an equation of two equal fractions. The primary way we solve a proportion is by using something called the cross-product. As you might already know you need to have great algebra skills to do well with ratios and proportions. I will be reviewing a good amount of the algebra skills you need in the lesson but if you need more help please go back and review ratios and proportions in your algebra notes. One thing that will be new to most students in this lesson is the property of ratios- this is usually not taught in Algebra 1 but you need to know it. I can t stress how important it is for you to be able to solve ratio and proportion problems as this will be the primary skill you will need for many more lessons. Good luck! Example Set C Ch. 7 Section 2 Similar Polygons In this section I will be teaching you about similar polygons. Similarity is a big topic in geometry so let s go ahead and give you a basic definition- two figures are similar if they have the same exact shape but not the same size. Think of a figure and a copy of a figure that has been zoomed out or zoomed in. The two figures would have exactly the same shape but different size/ lengths. One of the main concepts about similar figures is that there corresponding sides are in proportion. As such ratios and proportions are a core skill you must master to do well in this chapter. Many students confuse congruent figures and similar figures. Just a quick review- two congruent figures have the exact shape and size where two similar figures only have the exact shape but a different size. Please ensure that you have watched the lesson on ratios and proportions and have mastered how to set up ratios and solve proportion problems. Lastly make sure your notes are well organized and you practice everything we go over in the lesson. Example Set C Copyright 2014 TabletClass.com, LLC 27

28 Ch. 7 Section 3 Similar Triangles In this section I will teach you many important theorems and postulates about similar triangles. The concepts I m going to teach you require focus and concentration and are confusing to many students. Hence I suggest watching the video more than once just to ensure you understand all the theorems and postulates I cover. Some of these will be the AA Similarity Postulate, the SAS and SSS Similarity Theorems along with the Triangle Proportionality and Angle Bisector Theorems. Wow! I know it s a lot of material so take your time and work hard to master each concept. Please keep in mind that each one of these postulates and theorems are important and you can t skip learning a topic by just glancing at it to get a general idea. You need to practice, practice, and practice because this stuff is not that easy to fully comprehend. Also ensure you have watched the other lessons in this chapter before this one- especially the lesson on ratios and proportions. If you have a great attitude and really apply yourself you can ace this lesson. Example Set C Example Set D Copyright 2014 TabletClass.com, LLC 28

29 TabletClass Math Geometry Course Follow Along Guidebook Chapter 8 Chapter 8: Transformations In this chapter students will learn to apply transformations to images. Sections in the chapter focus on the transformations of reflections, rotations, dilations, translations and glide reflections. An emphasis is placed on developing the skills to construct the graphs of transformations found in common geometry problems. Section Summary (circle / complete after chapter is finished): 1. Reflections 2. Rotations and Dilations 3. Translations and Glide Reflections Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 29

30 Ch. 8 Section 1 Reflections In this section I will teach you about transformations and reflections. You can think of a transformation as taking the shape of a figure and moving it somewhere else on the x/y plane. The term we use for moving a figure is called mapping so a transformation is a where we map a figure to a different place on the x/y plane. What I just told you is a basic explanation of a transformation and there is a lot more to understand. One type of transformation is a reflection. Of course when we use the word reflection we think of a mirror. Now if you think about it a mirror image is an image that has been moved to another location- from the actual spot to a projected spot. The function of projecting an image to another place is the essence of what transformations are about. So after we learn about reflections we will look at other transformations in the next few lessons. Lastly you want to use graph paper and a ruler for this section as it involves lots of drawing. Pop quiz: can you solve a quadratic equation? Don t forget to keep doing a little algebra review as you study geometry. Example Set C Ch. 8 Section 2 Rotations and Dilations In this section I will teach you about rotations and dilations. Before you watch this video please ensure that you have watched the previous lesson on reflections. Rotations and dilations are types of transformations. As you know the first type of transformation we studied was the reflection. In this lesson we will continue our focus on transformations with rotations and dilations. A rotation is basically taking a figure and moving it clockwise or counterclockwise around a point. We use degrees to indicate a rotation so you may want to have a protractor for this lesson. A dilation is another type of transformation and it s a little more involved. What a dilation does is project a figure- like casting a shadow. For example think of a small figure being projected into a larger similar figure- this is a dilaltion. Of course the video will demonstrate these concepts much better. As always keep your notes nice and organized and practice as much as you can. Example Set C Copyright 2014 TabletClass.com, LLC 30

31 Ch. 8 Section 3 Translations and Glide Reflections In this section I will teach you about translations and glide reflections. Assuming you have watched the previous lessons in this chapter you know we are studying transformations. Recall a transformation is a mapping of a figure to another location. In the previous lessons we have looked at the transformations of reflections, rotations and dilations. Now we will explore another type of transformation called a translation. Wow I know the words transformation and translation are very similar so make sure to not to confuse the two. Ok what is a translation? Well a translation is a simple transformation such that we move a figure up or down or side to side. A glide reflection is a transformation where we first do a translation- then a reflection. Confused? Don t stress, the video will show this very clearly and I m sure you will understand. As in the other lessons you want to have graph paper and a ruler to practice the concepts. How do you like geometry so far? If you have watched and understood all the lessons to this point in the course you have a lot to be proud of- great work! Example Set C Copyright 2014 TabletClass.com, LLC 31

32 Chapter 9: Right Triangles and Trigonometry TabletClass Math Geometry Course Follow Along Guidebook Chapter 9 In this chapter students will learn a wide array of concepts about right triangles. Sections in the chapter look at similar right triangles, the Pythagorean Theorem and special right triangles. For most students the section on trigonometry will be their first introduction to the topic. The chapter ends on a section that applies right triangle trigonometry to solving word problems. Section Summary (circle / complete after chapter is finished): 1. Similar Right Triangles 2. The Pythagorean Theorem 3. Special Right Triangles 4. Trigonometric Ratios 5. Right Triangle Word Problems Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 32

33 Ch. 9 Section 1 Similar Right Triangles In this section I will teach you about similar right triangles. To master this topic you need to have a complete understanding of ratios and proportions- so please review if you need to before starting this video. The main concept in this lesson is that in every right triangle you can form 3 similar triangles. First let me stress that this theorem only applies to right triangles- those triangles that have a 90 degree angle. Next let s make sure you understand the term similar remember similar figures are those that have the exact same shape but a different size. The key point I want to stress is corresponding sides of similar figures are in proportion and we will be setting up a lot of ratios and proportions all through this lesson. You need to take your time with lesson and review the video at least once. In my experience many students struggle with this topic so you need to work hard at mastering it. As always take neat and organized notes and practice is a must for this lesson. Good luck! Example Set C Ch. 9 Section 2 The Pythagorean Theorem In this section I will teach you the Pythagorean Theorem. I can t overstate how important the Pythagorean Theorem is to all mathematics. The theorem provides much of the foundation of the study of geometry and trigonometry. Basically the Pythagorean Theorem gives us a way to find the lengths of right triangles. So many other theorems and formulas are based on the Pythagorean Theorem so you need to master it completely. As you will see in the lesson the theorem uses powers and square roots so having a calculator to work problems is suggested. Once you re done with the lesson you want to practice as many different type of problems you can- the earlier you master the formula the better. Example Set C Copyright 2014 TabletClass.com, LLC 33

34 Ch. 9 Section 3 Special Right Triangles In this section I will teach you about special right triangles. We will focus on two special right trianglesthe degree special right triangle and the degree special right triangle. I will be teaching you formulas that we can use to find the lengths of the sides of these special right triangles. These formulas are extremely important for you to learn. If you plan on going to college you will have to take the SAT or ACT test. I mention this because special right triangle problems are very common on these and other tests- trust me you need to master the skills in this lesson. Basically the formulas for special right triangles are ratios of the lengths of the sides of the triangle. Once you understand how the formulas work it s very easy to find the measure of all the sides of a special right triangle. Also because we are talking about right triangles you can use the Pythagorean Theorem as well to solve problems. Example Set C Ch. 9 Section 4 Trigonometric Ratios In this section I will teach you about trigonometric ratios. However for the most part you can think of this lesson as an introduction to trigonometry. I love trigonometry because it has so many practical applications and it combines algebra and geometry. Of course you may already know that trigonometry is its own subject and you we will be studying it in lots more detail if you continue your math education. One of the primary things I will be teaching you in the lesson is trigonometric ratios. Before I can teach you about these ratios I need to stress that trigonometry is based on right triangles. A trigonometric ratio is when we compare two sides of a right triangle forming a ratio. These ratios have names such as sine, cosine and tangent and they have dedicated functions on a scientific/graphing calculator. I hope you re excited about this lesson as you will learn some pretty powerful math. Also please ensure you have a scientific calculator you we need it for practice. Good luck and enjoy the video! Example Set C Example Set D Copyright 2014 TabletClass.com, LLC 34

35 Ch. 9 Section 5 Right Triangle Word Problems In this section I will teach you how to solve right triangle word problems. Now just to be clear there is no one exact procedure you can take to solve every word problem- there is however some general steps we want to follow to ensure success. Right triangle word problems will involve the use of trigonometric ratios and the Pythagorean theorem. As such you want to review these topics and make sure you know them well before watching this lesson. One of the smartest things you can do in solving any word problem is draw a sketch that models the problem. You don t have to draw a perfect picture for your sketch to have value. As long as you model the information in the problem in a neat and organized visual way then you will be one big step closer to solving the problem. As I said you will using trigonometric ratios to solve right triangle word problems so make sure you have a good scientific calculator. Lastly I can t stress how important it is to practice as many problems as you can- it s the only way you can guarantee you have mastered the skills and concepts Example Set C Copyright 2014 TabletClass.com, LLC 35

36 TabletClass Math Geometry Course Follow Along Guidebook Chapter 10 Chapter 10: Circles In this chapter students will learn the important properties and relationships found in circles. First, students will learn the parts of a circle and understand the properties of a tangent line. Additional sections will explore key theorems about arcs, chords and inscribed circles. Lastly, the chapter looks at other angle and segment relationships found in circles. Section Summary (circle / complete after chapter is finished): 1. Introduction to Circles and Tangents 2. Arcs and Chords 3. Inscribed Circles 4. Other Angle Relationships in Circles 5. Segment Lengths and Circles Post Chapter Checklist Extra Practice Problem Worksheet Completed Studied For Exam Chapter Test Score Date Taken Chapter Test (Retake) Score Date Taken Copyright 2014 TabletClass.com, LLC 36