Geometry

What you need to know, how to do it, and shortcuts to help

The main idea of this pamphlet

Now some of you may be thinking that Geometry is going to be boring, but it actually is not. Some of the big ideas in geometry include, tangible shapes, circles, finding lengths and proving congruency.


  • Chapter 6: Similar Figures
  • Chapter 7: Quadrilaterals
  • Chapter 8: Trig and Unit Circle
  • Chapter 9: Circles
  • Chapter 10: Volume

The Big Ideas of Geometry include:

  • Being able to understand measuring shaped and knowing properties that apply. Also, angle measures, and being able to find measures of angles and sides without tools, just with math.
  • Geometry is also concerned with relative shapes, congruency, with rigid motions and transformations.
  • Also, with the properties that make shapes what they are and how to prove them.

Chapter 6 : Similar Figures

Main Ideas:

  • Proofs- Being able to prove a therom or that something is indeed true through postulates and other reasons that have already been proven.
  • Similar Polygons- Showing that eventhough there is a difference in size their proportion may be the same. Also, they may be similar meaning that all their angles and all their side lengths are in proportion with each other.
  • Similar triangle Theroms- Reasons for which triangles are similar and they apply to all triangles, and can prove all triangles are similar.
  • Proving similar triangles-Almost the same thing as "Similar Triangle Theroms" but it is in a proof form.
  • Similar Triangles- Triangles that have proportional angle measures and proportional side measures.
  • Proportions- It basically means that the sides, angles, and the basic shape are all proportional to each other, meaning that their measures are relative in size.

Chapter 7: Quadrilaterals:

Main Ideas:


  • Theroms for proving Parallelograms- in this you use proof, earlier discussed in unit six to prove that the sides are parallel and also that the opposite angle are congruent
  • Quadrilaterals in the coordinate plane- In this you can prove that shapes are regular using the distance formula, slope, and y=mx+b form.
  • Finding the area of a parallelogram, Kite, Triangle, Rhombus, or Trapezoid- finding the area of these is useful in later units to find the volume of a solid which is useful in later units, like unit 10.


Chapter 8: Trigonometry

Main:


  • Pythagorean Therom- It is a way to figure out missing sides on right triangles
  • Finding missing angles and sides- This is when trig is necessary and also helpful in finding the missing angles and sides.
  • SOH-CAH-TOA- Sine Opposite Hypotenuse- Cosine Adjacent Hypotenuse- Tangent Opposite Adjacent
  • Using Trig in Everyday life- In everyday life trig can be used to find the hight of a building or even a mountain.
  • The Unit Circle- The unit circle uses coordinates to show angle measures and also radian measures.
  • General Angles and Radian Measures


Chapter 9: Circles

Main Ideas:


  • Proving that all circles are similar- this is true if you think about it because all the arcs are similar, and also because the general shape is similar
  • Finding angle measures- this is helpful because with this you can find angle measures and then you can find the measure of arcs as well.
  • Finding arc measure- the angle measure and also the arc measure go hand in hand, once you find one, you can find the other.
  • Finding inscribed angles- this means finding the measure of an angle inside the circle
  • Inscribed Quadrilaterals- learning the rules for finding the angle measures and such of a inscribed quadrilateral
  • Other angle relationships in Circles- general angle explanations about circles
  • Circimference and Arc length of circles- Finding the arc length and also circumference using known information
  • Finding the area of a sector- using what you know to find the area of a sector.







Chapter 10: Volume and Solid Figures

Main Ideas:


  • Finding the volume of solids- The simple area of the base times the height comes into play here, but it also goes much deeper than that.
  • Naming crossections - This is kind of hard to explain, but it basically means if you cut a solid down a line and what shape that will be. For example, if you cut a cone down a vertical line, the cross section would be a triangle.
  • Cavalieri's Principle- essentially states that if two prisms have the property that all corresponding cross sections have the same area, then those prisms have the same volume.
  • Using trig to find the area and later the volume of a solid- Sometimes it is necessary to use trig to find missing angle and side measures so that you can use those to find possibly the height of the solid or the area of the base.


What I Struggled With:

Short Cuts, Test Taking Strategies, and Tricks for remembering information

  • Trig: SOH-CAH-TOA. The first letter means the function, the next means the number on top, the last goes on the bottom.
  • Proofs, if you do not understand them, take you time to break them apart.
  • Test taking strategies:
  • Double check your work {I cannot tell you how many times I have caught simple mistakes that would have cost me percentage points.}
  • Copy down all of your work {even if your teacher does not give partial credit, you can still find your mistakes much easier if you show all of your work}

Videos That Helped Me

Geometry Help: 2-6 How to do a Geometric Proof
Two column proof showing segments are perpendicular
Geometry: 8-1 Similarity in Right Triangles
Geometry: 8-2 Trigonometric Ratios
Geometry: 3-5 Slopes of Lines
Geometry: 3-6 Lines in the Coordinate Plane

The Technology

Smore.com was great. I would recommend Smore.com to anyone who needed to do a project. It was very simple to use and it also made it very simple to insert videos, links, and photos. I had never heard of Smore.com before this project, but I will definately use it again. I like the simple layout of the Smore projects, sometimes I think other sites for presintations get a bit too concerned with the way the information is presented, instead of the information itself. I felt that Smore.com presented the information in a simple and easy to read fashion.

Sources

http://www.monroeschools.com/webpages/shammer/


Thanks to Ms. Hammer for the notes and also to google images for pictures