# Geometry Vocabulary and Notation

Geometry is made up of lines, lines segments, rays, angles, polygons, and circles.  It’s important to know what these basic geometry units are and how to name them, so that you understand geometry lessons, figures, and notation.  Often, the key to solving a geometry problems lies in understanding what the symbols mean.

Line: Lines are one dimensional figures that go on forever in both directions.  A line can be formed with any two points. In fact, any two points are colinear and any two points can form a line. When two lines intersect, they intersect at a point.

The figure above would be called "line AB" or "line BA" which is written $\overleftrightarrow{AB}$ or $\overleftrightarrow{BA}$

Line segment: Segments are pieces of lines that run between two points.

The figure above would be called "segment AB or BA" and written as $\overline{AB}$ or $\overline{BA}$

Ray: Rays are pieces of lines that stop at one point and go on forever in the other direction.  They are named with the end point first and the “never ending” point second.

The figure above would be called "ray AB" but not "ray BA" and is written only as $\overrightarrow{AB}$ NOT as $\overrightarrow{BA}$

Angle: Two rays or line segments that meet at a common end point (the vertex).

Plane: A plane is a two dimension shape that goes infinitely in four directions (imagine a piece of paper that goes out forever in every direction). Any three points are coplanar and any three points can form a plane. When two planes intersect, they form a line.

Polygon: Many sided, two dimensional figure.  Polygons include triangles, quadrilaterals, pentagons, and all figures with more than 3 straight lines as sides.

Regular: When a polygon is described as "regular," all if its sides are equal.

Perimeter: The distance around the outside edge of a polygon.

Area: The space inside the edges of a polygon.

Circle: A shape formed by one curved line that is equidistant from a center.

Circumference: The distance around the outside edge of a circle.

Area: The space inside the circle.

Radius: A line (any line) from the center of a circle to the edge (half of a diameter).

Diameter: A line (any line) that goes from edge to edge of a circle and passes through the center (two radii).

Union:  What separate (but touching or overlapping) lines, segments, or rays form when taken as one continuous line or segment. The symbol for union is: $\bigcup$

Intersection: Where two lines, segments, or rays overlap.  The symbol for intersection is: $\bigcap$

Bisect: Cut in half.  When line segments are bisected, they are cut into two equal line segments.  When angles are bisected, they are cut into two equal angles.

Midpoint: The point at the exact middle of a line segment.  The bisector crosses through the midpoint.  Segments on both sides of the midpoint are equal (and half the length of the full segment).

Symmetry: When both sides of a figure math. If you drew a line down the middle, the two sides would be mirror images.  The line is called a line of symmetry.

One of the main ways to test a student's geometry knowledge is to write a very simple problem that a student needs to understand to solve.

Example: You have $\overline{AB}$ that is bisected by $\overline{CD}$.  If Point C lies on $\overline{AB}$, and $\overline{AC}=20$, what is the length of $\overline{AB}$?

AB is a line segment.  CD not only crosses AB, but C is on AB and CD bisects AB.  That means that C lies exactly in the middle of AB. So, if the distance from A to C is 20, then the distance from AB is 40.

The key to this question is the word "bisect"!  Learn it!

Overall, good math students will know all of these words and be able to use them in simple and complicated math problems.