Geometry: Praxis I Exam

Updated on Jul 5, 2011

This section will familiarize you with the properties of angles, lines, polygons, triangles, and circles, as well as the formulas for area, volume, and perimeter.

Geometry is the study of shapes and the relationships among them. Basic concepts in geometry will be detailed and applied in this section. The study of geometry always begins with a look at basic vocabulary and concepts. Therefore, a list of definitions and important formulas is provided.

Geometry Terms

area the space inside a two-dimensional figure
circumference the distance around a circle
chord a line segment that goes through a circle, with its endpoints on the circle
congruent equal, in reference to lengths, measures of angles, or size of figures
diameter a chord that goes directly through the center of a circle—the longest line segment that can be drawn in a circle
hypotenuse the longest side of a right triangle, always opposite the right angle
leg either of the two sides of a right triangle that make the right angle
perimeter the distance around a figure
π (pi) the ratio of any circle's circumference to its diameter (pi is an irrational number, but most of the time it is okay to approximate π with 3.14)
radius a line segment from the center of a circle to a point on the circle (half of the diameter)
surface area the sum of the areas of all of a three-dimensional figure's faces
volume the space inside a three-dimensional figure

Coordinate Geometry

Coordinate geometry is a form of geometrical operations in relation to a coordinate plane. A coordinate plane is a grid of square boxes divided into four quadrants by both a horizontal x-axis and a vertical y-axis. These two axes intersect at one coordinate point, (0,0), the origin. A coordinate point, also called an ordered pair, is a specific point on the coordinate plane with the first number representing the horizontal placement and the second number representing the vertical placement. Coordinate points are given in the form of (x,y).

Coordinate Geometry

Graphing Ordered Pairs (Points)

  • The x-coordinate is listed first in the ordered pair and tells you how many units to move to either the left or the right. If the x-coordinate is positive, move to the right. If the x-coordinate is negative, move to the left.
  • The y-coordinate is listed second and tells you how many units to move up or down. If the y-coordinate is positive, move up. If the y-coordinate is negative, move down.
  • Example

    Graph the following points: (2,3), (3,–2), (–2,3), and (–3,–2).

    Graphing Ordered Pairs (Points)

  • Notice that the graph is broken up into four quadrants with one point plotted in each one. Here is a chart to indicate which quadrants contain which ordered pairs based on their signs:
  • Graphing Ordered Pairs (Points)

Lines, Line Segments, and Rays

A line is a straight geometric object that goes on forever in both directions. It is infinite in length, and is represented by a straight line with an arrow at both ends. Lines can be labeled with one letter (usually in italics) or with two capital letters near the arrows. Line segments are portions of lines. They have two endpoints and a definitive length. Line segments are named by their endpoints. Rays have an endpoint and continue straight in one direction. Rays are named by their endpoint and one point on the ray.

Lines, Line Segments, and Rays

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