Geometry Concepts: GED Test Prep (page 2)
This article reviews the geometry concepts you will need to know for the GED Mathematics Exam. You should become familiar with the properties of angles, lines, polygons, triangles, and circles, as well as the formulas for area, volume, and perimeter. A grasp of coordinate geometry will also be important when you take the GED.
Geometry is the study of shapes and the relationships among them. The geometry you are required to know for the GED Mathematics Exam is fundamental and practical. 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, here is a list of definitions of important terms.
- area—the space inside a two-dimensional figure
- bisect—cut in two equal parts
- circumference—the distance around a circle
- diameter—a line segment that goes directly through the center of a circle (the longest line you can draw in a circle)
- equidistant—exactly in the middle of
- hypotenuse—the longest leg of a right triangle, always opposite the right angle
- line—an infinite collection of points in a straight path
- point—a location in space
- parallel—lines in the same plane that will never intersect
- perimeter—the distance around a figure
- perpendicular—two lines that intersect to form 90-degree angles
- quadrilateral—any four-sided closed figure
- radius—a line from the center of a circle to a point on the circle (half of the diameter)
- volume—the space inside a three-dimensional figure
An angle is formed by an endpoint, or vertex, and two rays.
There are three ways to name an angle.
- An angle can be named by the vertex when no other angles share the same vertex: A.
- An angle can be represented by a number written across from the vertex: 1.
- When more than one angle has the same vertex, three letters are used, with the vertex always being the middle letter: 1 can be written as BAD or as DAB; 2 can be written as DAC or as CAD.
Angles can be classified into the following categories: acute, right, obtuse, and straight.
- An acute angle is an angle that measures less than 90 degrees.
- A right angle is an angle that measures exactly 90 degrees. A right angle is represented by a square at the vertex.
- An obtuse angle is an angle that measures more than 90 degrees, but less than 180 degrees.
- A straight angle is an angle that measures 180 degrees. Thus, both of its sides form a line.
Two angles are complementary if the sum of their measures is equal to 90 degrees.
Two angles are supplementary if the sum of their measures is equal to 180 degrees.
Adjacent angles have the same vertex, share a side, and do not overlap.
The sum of all of the measures of adjacent angles around the same vertex is equal to 360 degrees.
Angles of Intersecting Lines
When two lines intersect, two sets of nonadjacent angles called vertical angles are formed. Vertical angles have equal measures and are supplementary to adjacent angles.
- m1 = m3 and m2 = m4
- m1 = m4 and m3 = m2
- m1 + m2 = 180 and m2 + m3 = 180
- m3 + m4 = 180 and m1 + m4 = 180
Bisecting Angles and Line Segments
Both angles and lines are said to be bisected when divided into two parts with equal measures.
Line segment AB is bisected at point C.
According to the figure, A is bisected by ray AC.
Angles Formed by Parallel Lines
- When two parallel lines are intersected by a third line, vertical angles are formed.
- Of these vertical angles, four will be equal and acute, and four will be equal and obtuse.
- Any combination of an acute and an obtuse angle will be supplementary.
In the previous figure:
- b, c, f, and g are all acute and equal.
- a, d, e, and h are all obtuse and equal.
- Also, any acute angle added to any obtuse angle will be supplementary.
mb + md = 180°
mc + me = 180°
mf + mh = 180°
mg + ma = 180°
In the following figure, if m||n and a||b, what is the value of x?
Because both sets of lines are parallel, you know that x° can be added to x + 10 to equal 180. The equation is thus x + x + 10 = 180.
Solve for x:
Therefore, mx = 85 and the obtuse angle is equal to 180 – 85 = 95.
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