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Area and Perimeter

The area of a figure measures the size of the space it takes up. It is always, always measuring a flat surface. To find the area of something, you must multiply length and width. This is usually put in some type of square unit. Some examples of the units used are square meters, square centimeters, square inches, or square kilometers.

Perimeter is the sum of all the sides of a shape. This is related to area, so you can also use meters, centimeters, inches or kilometers.

Figures and Shapes

A polygon must have the features below:

• no gaps


• straight lines


• 3 or more sides

Here are some polygons:

There are 2 types of polygons, regular polygons and irregular polygons. Regular polygons have all the same sized sides while irregular polygons have different sized sides.

Shapes

Triangle:

3 sides

Types:

• Scalene Triangle
• Acute Triangle
• Obtuse Triangle
• Right Triangle
• Equilateral Triangle
• Isosceles Triangle

Quadrilateral:

4 sides

Types:

• Rectangle
• Square

Parallelogram:

4 sides

Types:

• Rhombus
• Trapezoid

Basic Shapes:

Any amount of sides

Types:

• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
• Decagon
• Circle

There are many ways to describe a shape, for instance, convex figures go outward and concave figures go inward.

In this lesson, we have learned about shapes and figures, in the next lesson, we will learn about measurement.

What is an Angle?
An angle is two rays that share the same endpoint, the point where they intersect is called the vertex. The two rays are called the sides of the angle.

Here are some angles:

There are many types of angles:

Acute Angles are cute and small:

Obtuse Angles are big and of course obese:

A right angle is an angle measuring 90 degrees. It is two lines or line segments that meet at a right angle and are to be perpendicular:

Complementary angles are two angles that sum up to 90 degrees:

Supplementary angles are two angles that sum up to 180 degrees:

Measuring Angles

To measure an angle, we must use a device called a protractor, a protractor uses units called degrees. Measuring an angle is really easy!

Vertical Angles are two lines that meet,vertical angles have the same degree for each side.

For example, a few vertical angles are listed below:

Now that we have learned about vertical angles, we must learn about what they make. When they cross over, of course they make an angle, but what are these called? Well, some vertical angles make right angles, any right angle that a vertical angle forms is called a perpendicular line.

We have learned our second session, next, we will learn about shapes and figures. Enjoy!

Geometry and Spatial Reasoning

What is geometry?
To start off, I would like to say that geometry is quite simple if you put your mind into it. Geometry is another way of saying "the study of shapes" or.... obj.3. Geometry is the study of shapes and configurations. It classifies spaces in figures and shapes.



The Types of Geometry and What They Are

There are many ways to classify geometry, there are also many types of geometry. One type of geometry is Euclidean geometry, Euclidean geometry has to do with the study of a flat surface or flat shapes. Then, there is Riemannian geometry which deals with the study of curved objects like the surface of a sphere. If you would put these 2 types of geometry together, I would say that Riemannian geometry is much harder than Euclidean geometry because it is hard to study and measure out curved surfaces, but both are the same important.

Here are some other types of geometry that are important too:

• Differential geometry is geometry that relates to calculus algebra, it is in the simplest form of calculus......vector calculus.


• Algebraic geometry studies objects dealing with polynomial equations. Algebraic geometry is in comparison to the recent solutions for many difficult problems in math.


• Semi-Riemannian geometry was what Albert Einstein used to study the four dimensional geometry of time and space.



• Symplectic geometry is from the study of the evolution of simple mechanical systems, but now imbues all features of theoretical physics.
  

What are the basic terms in geometry?

Now that we know that geometry is dealing with shapes, we must learn about the terms in geometry. One of the most common terms in geometry is lines, think about it, hmm.... when lines come to mind, we think of the straight lines we draw on paper, but in geometry lines go on forever. To draw a line in geometry, we couldn't possibly draw the line going on forever, that would take way too long, so you would just draw arrows at the end of both points on a short line.

For example look at the line below:









Now for the line segment. The line segment is what it is called, part of a line. Points are the things that end a line segment. A point looks exactly like a dot, to identify a point, you must use a number or letter. Points don't exactly have anything to do with measurement, but they do play an important role in geometry by ending a line segment.


Example:

Now, you may be wondering, hmm, if we combined a line segment and a line, what would we get, well, the answer to that question is quite simple, you would get, of course, a ray. A ray is a straight line that begins at a certain point and extends forever in one direction. The point where the ray starts is called it's endpoint. This is like a line on one side ( with the arrow) and a line segment on the other (there is a point).

For example, look at the ray below:

Since we have learned about lines, line segments, and rays we will learn about what happens when they meet, this is intersection. The term intersect is used when lines, line segments, rays, or figures meet, this is when they share a point/vertex . We say that these figures intersect or cross over.


For Example look at the intersection below:

There is also another thing you need to know. Intersection isn't the only way two lines come together. There also is a little something called "parallel lines". Two lines in the same plane that don't intersect are called parallel lines. 2 line segments are parallel if the lines that they are on are parallel.

• If line 1 is parallel to line 2, it is wrote like this:

line 1line 2

• When two line segments MJ and FH are on parallel lines, we write them like this:

segment MJ segment FH.

For example, look at the 2 parallel lines below:








Well, that is the end of the lesson about lines and terms, now, lets move on to the next part.........ANGLES!