Fall Geometry Essentials
Basic Geometric Concepts
The Building Blocks
Geometry starts with a few simple ideas. The most basic is the point. A point is just a location in space. It has no size, no width, and no depth. Think of it as the tiniest dot you can imagine, and then imagine it even smaller.
If you string an infinite number of points together in a straight path, you get a line. A line is perfectly straight and goes on forever in both directions. The arrows on each end show that it never stops.
Now, imagine a flat surface, like a sheet of paper, that also extends forever in all directions. That's a plane. It has length and width but no thickness. Points and lines exist on planes.
Parts of a Line
While a line goes on forever, we often work with smaller pieces of it.
A line segment is a part of a line with two endpoints. It has a definite start and end, which means you can measure its length.
A ray is a mix of the two. It has one endpoint and extends infinitely in the other direction. A ray of sunlight is a good way to picture it: it starts at the sun and travels on and on.
When Lines Meet
When two rays share a common endpoint, they form an angle. The endpoint is called the vertex, and the two rays are the sides of the angle. We measure angles in degrees, represented by the symbol °. A full circle has 360°.
Angles can be classified by their size.
An acute angle is a sharp angle, measuring less than 90°. A right angle is a square corner, measuring exactly 90°. It's often marked with a small square at the vertex. An obtuse angle is a wide angle, measuring more than 90° but less than 180°.
A straight line is also an angle, called a straight angle. It measures exactly 180°.
Angle Pairs
Sometimes, angles work together in pairs. Two common relationships are complementary and supplementary.
Complementary
adjective
Two angles whose measures add up to 90°.
Supplementary
adjective
Two angles whose measures add up to 180°.
These basic elements and relationships are the alphabet of geometry. By understanding them, you can start to describe and analyze the shapes and spaces all around us.
What is the fundamental building block of geometry, representing a single location in space with no dimensions?
A beam of light from a laser pointer, starting at the device and traveling outward, is a real-world example of a...
