The Fundamentals of Geometry Study Guide
Introduction to The Fundamentals of Geometry
The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.
—ARISTOTLE, Greek philosopher (384 b.c.e.–322 b.c.e.)
Geometry typically represents only a small portion of most standardized math tests. The geometry questions that are included tend to cover the basics: points, lines, planes, angles, triangles, rectangles, squares, and circles. You may be asked to determine the area or perimeter of a particular shape, the size of an angle, the length of a line, and so forth. Some word problems may also involve geometry. And, as the word problems will show, geometry problems come up in real life as well.
Points, Lines, and Planes
What Is a Point?
A point has position but no size or dimension. It is usually represented by a dot named with an uppercase letter:
What Is a Line?
A line consists of an infinite number of points that extend endlessly in both directions.
A line can be named in two ways:
- By a letter at one end (typically in lowercase): l
- By two points on the line:
The following terminology is frequently used on math tests:
||Points are collinear if they lie on the same line. Points J,U,D, and I are collinear.|
||A line segment is a section of a line with two endpoints. The line segment at right is indicated as .|
||The midpoint is a point on a line segment that divides it into two line segments of equal length. M is the midpoint of line segment .|
||Two line segments of the same length are said to be congruent. Congruent line segments are indicated by the same mark on each line segment. are congruent. are congruent. Because each pair of congruent line segments is marked differently, the four segments are NOT congruent to each other.|
||A line segment (or line) that divides another line segment into two congruent line segments is said to bisect it. bisects .|
What Is a Plane?
A plane is like a flat surface with no thickness. Although a plane extends endlessly in all directions, it is usually represented by a four-sided figure and named by an uppercase letter in a corner of the plane: K.
Points are coplanar if they lie on the same plane.
Points A and B are coplanar.