Geometry began with a study of measurement on objects' size, relative position and space on the Earth. As most of our actions take place on Earth, we need to understand geometry. In addition, geometry also provides a vigorous training on use of logic in presentation and discussion of ideas.
Basic terminologies and concepts
Here are some basic terminologies and concepts in studying geometry.
- Point - basic element of geometry which represents an object without any size. It is the abstraction of things like the tip of a needle, a pencil, a mark drawn by a pencil ...
- Line segment - a line segment is an object with no width and height but has a finite length. If you draw two distinct points (the end points) using a pencil and connect them together, the object formed is a line segment.
- Line - a line is an object with no width and height but has an infinite length. If we extend the line segment drawn in the above indefinitely, we get a line.
- Straight or curve - a line segment or line is called straight if it is constructed in a way such that the direction is not changed. Otherwise, it is called a curve.
- Ray - a ray is an object which is obtained by extending only one end point of a line segment indefinitely. The other end point is kept fixed.
- Angle - an angle is an object formed by having two rays with the same fixed end point.
The following diagram shows the objects discussed above. Can you identify them?
Exploration of different types of angle
As you move the point C or A in the above simulation, you can see that the angle \(\alpha\) changes its size. Angles are named according to their sizes. Angle size is commonly measured by degree. For a complete round (a circle), named round angle, is arbitrarily assigned to be 360 degrees, symbolically \(360^o\). For finer measurement, we define 1 degree to be composed of 60 minutes and 1 minute to be composed of 60 seconds. This is very similar to our time system.
Based on this, the following commonly named angles are defined as the size of the angle \(\alpha\) increased:
- acute angle
- right angle
- obtuse angle
- straight angle
- reflex angle
Use the computer simulation below to learn how to measure and explore the above named angles.