The word geometry is Greek for geos - meaning earth andmetron - 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.
Terms (Undefined) 1. Point
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.

2. 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.
Terms (Defined) 1. 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. 2. Ray
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: 3. Angle
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. 4. Plane
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. An angle is defined as: where two rays or two line segments join at a common endpoint called the vertex. See part 1 for additional information.
Acute Angle
An acute angle measures less that 90° and can look something like these (angles between the grey rays):

Right Angle
A right angle measures exactly 90° and will look something like this:

Obtuse Angle
An obtuse angle measures more than 90° but less than 180° and will look something like these:

Straight Angle
A straight angle is 180°

Reflex Angle
An reflex angle is more than 180° but less than 360° and will look something like this:

Pairs of Angles:
Complementary Angles
Two angles adding up to 90° are called complementary angles. | ABD + DBC are Complementary |
Supplementary Angles
Two angles adding up to 180° are called supplementary angles. | ABD + DBC are Supplementary |
If you know the angle of ABD, you can easily determine what the DBC is by subtracting ABD from 180!
Background:
Euclid of Alexandria wrote 13 books called 'The Elements' around 300 BC. These books laid the foundation of geometry. Some of the postulates below were actually posed by Euclid in his 13 books. They were assumed as axioms, without proof. Euclid's postulates have been slightly corrected over a period of time. Some are listed here and continue to be part of 'Euclidean Geometry'.

Know this stuff! Learn it, memorize it and keep this page as a handy reference if you expect to understand Geometry.
There are some basic facts, information and postulates that are very important to know in geometry. Not everything is proved in Geometry, thus we use some postulates which are basic assumptions or unproved general statements that we accept. Here are a few of the basics and postulates that are intended for entry level Geometry. (Note: there are many more postulates than are stated here, these postulates are intended for beginner geometry)
The Basics and Important Postulates :
1. You can only draw one line between two points. You will not be able to draw a second line through points A and B:

2. There's 360° around a circle.

3. Two lines can instersect at ONLY one point. S is the only intersection of and in the figure below.

4. A line segment has ONLY one midpoint. M is the only Midpoint of in the figure below.

5. An angle can only have one bisector. (Bisector: a ray that's in the interior of an angle and forms two equal angles with the sides of that angle.)
In the figure below, is the bisector of A

6. Any geometric shape can be moved without changing its shape.

7. A line segment will always be the shortest distance between two points on a plane. The curved line and the bropken line segments are further in distance between A and B.

8. If two points lie in a plane, the line containing the points lie in the plane.
9. When two planes intersect, their intersection is a line.
10. ALL lines and planes are sets of points.
11. Every line has a coordinate system. (The Ruler Postulate)
Solid geometry is concerned with three-dimensional shapes. Some examples of three-dimensional shapes are cubes, rectangular solids, prisms, cylinders, spheres, cones andpyramids. We will look at the volume formulas and surface area formulas of the solids. We will also discuss some nets of solids.

Cubes
A cube is a three-dimensional figure with six matching square sides.

The figure above shows a cube. The dotted lines indicate edges hidden from your view.
If s is the length of one of its sides, then the volume of the cube is s × s × s
Volume of the cube = s3
The area of each side of a cube is s2. Since a cube has six square-shape sides, its total surface area is 6 times s2.
Surface area of a cube = 6s2
Worksheet to calculate volume and surface area of cubes.

More examples about the volume of cubes.
More examples about the surface area of cubes.

Rectangular Solids or Cuboids
A rectangular solid is also called a rectangular prism or a cuboid.
In a rectangular solid, the length, width and height may be of different lengths.

The volume of the above rectangular solid would be the product of the length, width and height that is
Volume of rectangular solid = lwh
Total area of top and bottom surfaces is lw + lw = 2lw
Total area of front and back surfaces is lh + lh = 2lh
Total area of the two side surfaces is wh + wh = 2wh
Surface area of rectangular solid = 2lw + 2lh + 2wh = 2(lw + lh + wh)
Points, Lines, and Planes
Point, line, and plane, together with set, are the undefined terms that provide the starting place for geometry. When we define words, we ordinarily use simpler words, and these simpler words are in turn defined using yet simpler words. This process must eventually terminate; at some stage, the definition must use a word whose meaning is accepted as intuitively clear. Because that meaning is accepted without definition, we refer to these words as undefined terms. These terms will be used in defining other terms. Although these terms are not formally defined, a brief intuitive discussion is needed.
Point
A point is the most fundamental object in geometry. It is represented by a dot and named by a capital letter. A point represents position only; it has zero size (that is, zero length, zero width, and zero height). Figure 1 illustrates point C, point M, and point Q.

| | | | | | Figure 1 | Three points. | | |
Line
A line (straight line) can be thought of as a connected set of infinitely many points. It extends infinitely far in two opposite directions. A line has infinite length, zero width, and zero height. Any two points on the line name it. The symbol ↔ written on top of two letters is used to denote that line. A line may also be named by one small letter (Figure 2 ).

| | | | | | Figure 2 | Two lines. | | |
Collinear points
Points that lie on the same line are called collinear points. If there is no line on which all of the points lie, then they are noncollinear points. In Figure 3 , pointsM, A, and N are collinear, and points T, I, and C are noncollinear.

| | | | | | Figure 3 | Three collinear points and three noncollinear points. | | |
Plane
A plane may be considered as an infinite set of points forming a connected flat surface extending infinitely far in all directions. A plane has infinite length, infinite width, and zero height (or thickness). It is usually represented in drawings by a four-sided figure. A single capital letter is used to denote a plane. The word plane iswritten with the letter so as not to be confused with a point (Figure 4 ).

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Kinds of angles according to size? acute angle = less than 90o & greater than 0o right angle = 90o obtuse angle = greater than 90o & less than 180o straight angle = 180o reflex angle = greater than 180o

Constructing different angles and shapes
In this lesson, we will look at constructing different angles and shapes using compasses * A 90˚ angle can be obtained by constructing a perpendicular bisector. * A 45˚ angle can be obtained by bisecting a 90˚ angle. * A 22.5˚ angle can be obtained by bisecting a 45˚ angle. * A 60˚ angle can be obtained by constructing an equilateral triangle. * A 30˚ angle can be obtained by bisecting a 60˚ angle. * A 15˚ angle can be obtained by bisecting a 30˚ angle.
Congruent line segments * Two line segments are congruent if they have the same length. But they need not lie at the same angle or position on the plane.
See Congruent Line Segments Parallel Lines | | Two lines on a plane that never meet. They are always the same distance apart.Skew LinesDefinition of Skew LinesTwo nonparallel lines in space that do not intersect are called skew lines.Examples of Skew Lines are skew lines in the figure shown. |
Perpendicular lines
Two lines that intersect and form right angles are called perpendicular lines. The symbol ⊥ is used to denote perpendicular lines. In Figure 2 , line l ⊥ line m.

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transversal
In geometry, a transversal is a line that passes through two parallel lines in the same plane at different points. When the lines are parallel, as is often the case, a transversal produces several congruent and several supplementary angles. When three lines in general position that form a triangle are cut by a transversal, the lengths of the six resulting segments satisfy Menelaus' theorem.