The word geometry is Greek for geos - meaning earth and metron - meaning measure. Geometry was extremely important to ancient societies and was used for surveying, astronomy, navigation, and building. Geometry, as we know it is actually known as Euclidean geometry which was written well over 2000 years ago in Ancient Greece by Euclid, Pythagoras, Thales, Plato and Aristotle just to mention a few. The most fascinating and accurate geometry text was written by Euclid, and was called Elements. Euclid's text has been used for over 2000 years!
Geometry is the study of angles and triangles, perimeter, area and volume. It differs from algebra in that one develops a logical structure where mathematical relationships are proved and applied. In part 1, you will learn about the basic terms associated with Geometry.
Points show position. A point is shown by one capital letter. In the example below, A, B, and C are all points. Notice that points are on the line.
A line is infinite and straight. If you look at the picture above, is a line, is also a line and is a line. A line is identified when you name two points on the line and draw a line over the letters. A line is a set of continuous points that extend indefintely in either of its direction. Lines are also named with lowercase letters or a single loswer case letter. For instance, I could name one of the lines above simply by indicating an e.
- Line Segment
A line segment is a straight line segment which is part of the straight line between two points. To identify a line segment, one can write AB or . The points on each side of the line segment are referred to as the end points.
A ray is the part of the line which consists of the given point and the set of all points on one side of the end point.
A is the end point and this ray means that all points starting from A are included in in the ray. A ray can also be written like:
An angle can be defined as two rays or two line segments having a common end point. The endpoint becomes known as the vertex. An angle occurs when two rays meet or unite at the same endpoint.
The angles pictured below can be identified as ABC or CBA. You can also write this angle as B which names the vertex. (common endpoint of the two rays.)
The vertex (in this case B) is always written as the middle letter. It matters not where you place the letter or number of your vertex, it is acceptable to place the it on the inside or the outside of your angle.
This angle would be called 3. OR, you can also name the vertex by using a letter. For instance, 3 could also be named angle B if you choose to change the number to a letter.This angle would be named ABC or CBA or B
Note: When you are referring to your text book and completing homework, make sure you are consistent! If the angles you refer to in your homework use numbers - use numbers in your answers. Which ever naming convention your text uses is the one you should use.
A plane is often represented by ablackboard, bulletin board, a side of a box or the top of a table. These 'plane' surfaces are used to connect any two or more points on a straight line. A plane is a flat surface.
You are now ready to move to:
Part 2: Types of Angles