Marked June 7th

Revised By : Haley F.,Erin S. and Joel B.

Geometry is the basic unit for measuring an object. To understand the principles of geometry, this unit examines: size, angles, the relationship of lines, diagonal point, median point, midpoint, shapes, bisecting of lines and determining the properties of composite shapes. Geometry has grown into our everyday lives and we continue to use this mathematical unit without even knowing it. With the expansion of technology, we are able to use math more effectively every day and use it to help us continue to move forward.

-Geometry was discovered by a man, in the year 300 B.C., named Euclid.

external image 225px-Euklid-von-Alexandria_1.jpg

euclid_colour.jpg
Euclid



Angles

Angles are one of the many types of geometry. An acute angle is an angle that is less than 90 degrees but more than zero. A right angle is an angle that is exactly 90 degrees. An obtuse angle is an angle that is over 90 degrees but under 180.
external image 783px-Acute_Angle_%28PSF%29.svg.pngexternal image Obtuseangle.jpg

external image 335px-Reflex_angle,_numbers.svg.pngexternal image straightangle.jpg

Reflex Angles are angles over 180 degrees but under 360, while straight angles are exactly 180 degrees.
Geometry is the study of shapes. This involves the number of sides, the angles, the shape itself, and of course the area and perimeter.
external image geometry_tools_kpyf.gifexternal image geometry-tools.gifexternal image 42-17674521.jpg?size=572&uid=%7B4290AC77-815D-4BCB-BDF0-EFD1AB6395EC%7D


When using geometry properly (Hendriks) you can use any of these methods mentioned above to calculate or measure the data of a shape.

Here are some examples of shapes:

Squares are Rectangles
Cubes are Rectangular Prisms
pulsating_rectangles.gif
square.gifRectangles.JPG


cube.jpgexternal image Necker%20Cube.jpgexternal image 339856868_f711a5c8aa.jpg


Circles,Triangle

circles.JPG triangle.jpgtriangle.gifexternal image 20080110-optical-illusion-circles.jpg


Midpoint, Median, Diagonal

(Hendriks)


Midpoint:

  • A point on a line segment that is located exactly between the two endpoints.

external image pic2.gif

Median


  • A line segment that joins a vertex of a triangle to the midpoint of the opposite side.
external image median.gif






Diagonal

  • A line segment joining two non-adjacent vertices of a polygon with four or more sides.

external image diagonal.gif



BISECTING AN ANGLEbisect.jpg


To bisect an angle using a compass you have to:
1. Put the pointed end of the compass on the point (vertex) of the angle

2. Then draw a line a bit more than halfway up,
make sure it touches the lines.

3.Put the pointed end of the compass on the
point where the two lines intersect then draw
a small curved line. Repeat this step for the
other side so the small lines cross.

4.Draw a line from the point of the angle to
where the small curved lines cross. Finally,
the line has been bisected.







Go to this website to watch how to bisect an angle:
http://www.mathopenref.com/constbisectangle.html


INTERESTING FACTS


- the midpoints of two sides of a triangle, has a line segment that is joined in parallel to the third side of the triangle and half as long.
- the area of the triangle is cut in half by the medians of that triangle.
- a quadrilateral prodcues a parallelogram by joining the midpoints of the sides.
- the diagonals of any parallelogram interesect/cross each other in such a way that each diagonal's length is cut in half. That is, the diagonals of
any parallelogram bisect each other. (Hendriks)




GEOMETRY IN THE REAL WORLD

You may think math is one of the most boring subjects on Earth, and geometry is no different. However, did you know there are tons of jobs out there that require this tedius task? And maybe, just maybe, it's not so boring when you apply what you know to the real world?
For example, jobs can be as simple as tiling/carpeting your home, where you need proper measurements of areas in your homes, as each wall has a corner, therefore requiring the measurments of angles.
Working with scaffolding uses alot of angles. In order to make a structure out of scaffolding safe, proper angles must be used to support all the pieces.

Even as a chef, you must use geometry. What shape of pan should I use? How big should the pot be?
Anybody who has to make something must use geometry. If you are making a coffee table, you must use the right shape, and get the proper angles to make a sturdy table.
An interior designer must use geometry. How much space do I have to work with? How big are my pieces? How do I get them all to fit nicely in here?
As well, construction workers have to make sure they have enough wood to properly sustain a building, so it is sturdy enough for people, in large quantities, to walk on.
With the economy continuing to grow there are jobs in urban land design. For example, construction workers need to know what the streets are like. Are the streets curved? Are the streets straight?
Roof industries have lots of angles to work with, when developing a roof or putting shingles on a roof, concidering that most roofs take on the shape of a triangle and consist of many angles. Therefore they need to find the midpoint and medians of each of the shapes that the roof is made up of.
As technology continues to enhance each year, math is being used in computer science. Building the computer as a product takes lots of time and math. There are small pieces/parts that must be attatched or linked together, by sometimes bisecting lines and finding the midpoints and median of a line.



Work Cited



Hendriks, J.D. (2008). MPM 1D1 - Course Notes
video for midpoint/median - www.youtube.ca