My Final Words and Thoughts on Geometry...

 

 

People, it's really not that bad, i promise!

Time and time again I have heard people groan, sigh, and complain loudly about learning geometry. These actions were usually accompanied by eye rolling, pencil throwing, mumbling obscenities under one's breath, or other angry gestures. Not only is learning geometry not that bad, it is also extremely important because we can utilize it in the real world (unlike most algebra in my opinion...*cough)

Geometry has a purpose, and that purpose is to help us understand the world around us. Believe it or not lines, points, and shapes are extremely important and relevant. Without learning about these things we would be unable to build, design architecture or half of the things we use on a daily basis.

 

 Take a deep breath and relax...geometry is not the end of the world. :)

 

Sincerely, your friend and confidant

Nina Owens

 

Quadrilaterals!

A polygon with four sides (or edges) and four vertices or corners.

Types of Quadrilaterals:

 

*Trapezoids- at least one parallel side

*Kite- two adjacent sides the same, and the other two sides are also the same

*Parallelogram- each pair of opposite sides is parallel

*Rectangle- Parallelogram with a right angle

*Rhombus- Parallelogram with 2 adjacent sides that are equal

*Square- a rectangle with two adjacent sides that are the same

Also, I had to.... 

  haha :)

Types of Triangles!

There are several types of triangles in geometry:

Obtuse triangle-containing one obtuse angle

       Acute triangle- all angles are acute

Right triangle- containing one angle that equals 90 degrees (right angle)

Triangles based on size of sides:

Scalene- triangle with no sides that are the same.

Isosceles- At least two sides are the same.

Equilateral- All sides are exactly the same.

Now onto polygons!

...No, not Porygon from Pokemon

But they do have a lot in common!

You see, Polygons are simply shapes. And Porygon is made completely from different shapes. Hey, it helps me remember ;)

 

Polygons are shapes, all different sizes. They are simple closed curves with sides that are line segments.

Convex and Concave Shapes

How i like to remember the difference between the two, is that concave shapes are caving in, while the convex shapes have structure and do not cave in.

Now onto angles!

 

An angle is formed by two rays with the same endpoint.

The vertex of an angle is the common endpoint of the two rays that form an angle.

Adjacent angles are those that share a common side and vertex, but do not overlap:

*Different types of angles*

 

Straight angle- exactly 180 degrees 

Obtuse angle- greater than 90 degrees but less than 180 degrees

Acute angle- less than 90 degrees

Right angle - measures exactly 90 degrees

 

 

Lines, Points, and Planes

 

 

Let's begin with the basic building block of geometry...lines! Without lines an shape would not be able to exist!

A straight line extends forever, and always equals 180 degrees as seen above.

 A line segment is a portion of a line, that ends in two points creating the segment.

A ray starts from one single point and extends into one direction only.

An angle is created by 2 rays extending from a single point.

Intersecting lines cross each other and have exactly one point in common.

Parallel lines NEVER cross, and have no points in common.

Lastly we have perpendicular lines that form a right angle of 90 degrees!

So what exactly is Geometry anyway?

It is defined as the following:

ge·om·e·try  

/jēˈämitrē/

Noun

1. The branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. 

So, in summation we will be discussing topics of different shapes, lines, angles, and degrees of angles!

Lets get started shall we?