Basic Math and Pre-Algebra For Dummies (76 page)

Angles that have fewer than 90° — that is, angles that are sharper than a right angle — are called
acute angles
, like this one:

Angles that measure greater than 90° — that is, angles that aren't as sharp as a right angle — are called
obtuse angles
, as seen here:

When an angle is exactly 180°, it forms a straight line and is called a
straight angle
.

A shape is any closed geometrical figure that has an inside and an outside. Circles, squares, triangles, and larger polygons are all examples of shapes.

Much of plane geometry focuses on different types of shapes. In the next section, I show you how to identify a variety of shapes. Later in this chapter, I show you how to measure these shapes.

 A
shape
is any closed two-dimensional (2-D) geometrical figure that has an inside and an
outside
, separated by the
perimeter
(boundary) of the shape. The area of a shape is the measurement of the size inside that shape.

A few shapes that you're probably familiar with include the square, rectangle, and triangle. However, many shapes don't have names, as you can see in Figure 
16-1
.

Measuring the perimeter and area of shapes is useful for a variety of applications, from land surveying (to get information about a parcel of land that you're measuring) to sewing (to figure out how much material you need for a project). In this section, I introduce you to a variety of geometric shapes. Later in the chapter, I show you how to find the perimeter and area of each, but for now, I just acquaint you with them.

A
polygon
is any shape whose sides are all straight. Every polygon has three or more sides (if it had fewer than three, it wouldn't really be a shape at all). Following are a few of the most common polygons.

The most basic shape with straight sides is the
triangle
, a three-sided polygon. You find out all about triangles when you study trigonometry (and what better place to begin than
Trigonometry For Dummies
, 2nd Edition, by Mary Jane Sterling [Wiley]?). Triangles are classified on the basis of their sides and angles. Take a look at the differences (and see Figure 
16-2
):

• Equilateral:
  An
  equilateral triangle
  has three sides that are all the same length and three angles that all measure 60°.
  
• Isosceles:
  An
  isosceles triangle
  has two sides that are the same length and two equal angles.
  
• Scalene:
  Scalene triangles
  have three sides that are all different lengths and three angles that are all unequal.
  
• Right:
  A
  right triangle
  has one right angle. It may be isosceles or scalene.
  

A
quadrilateral
is any shape that has four straight sides. Quadrilaterals are one of the most common shapes you see in daily life. If you doubt this statement, look around and notice that most rooms, doors, windows, and tabletops are quadrilaterals. Here I introduce you to a few common quadrilaterals (Figure 
16-3
shows you what they look like):

• Square:
  A
  square
  has four right angles and four sides of equal length; also, both pairs of opposite sides (sides directly across from each other) are parallel.
  
• Rectangle:
  Like a square, a
  rectangle
  has four right angles and two pairs of opposite sides that are parallel. Unlike the square, however, although opposite sides are equal in length, sides that share a corner —
  adjacent
  sides — may have different lengths.
  
• Rhombus:
  Imagine starting with a square and collapsing it as if its corners were hinges. This shape is called a
  rhombus.
  All four sides are equal in length, and both pairs of opposite sides are parallel.
  
• Parallelogram:
  Imagine starting with a rectangle and collapsing it as if the corners were hinges. This shape is a
  parallelogram —
  both pairs of opposite sides are equal in length, and both pairs of opposite sides are parallel.
  
• Trapezoid:
  The
  trapezoid
  's only important feature is that at least two opposite sides are parallel.
  
• Kite:
  A kite is a quadrilateral with two pairs of adjacent sides that are the same length.
  

 A quadrilateral can fit into more than one of these categories. For example, every parallelogram (with two sets of parallel sides) is also a trapezoid (with at least one set of parallel sides). Every rectangle and rhombus is also both a parallelogram and a trapezoid. And every square is also all five other types of quadrilaterals. In practice, however, it's common to identify a quadrilateral as descriptively as possible — that is, use the
first
word in the list that accurately describes it.

A polygon can have any number of sides. Polygons with more than four sides aren't as common as triangles and quadrilaterals, but they're still worth knowing about. Larger polygons come in two basic varieties: regular and irregular.

A
regular polygon
has equal sides and equal angles. The most common are regular pentagons (five sides), regular hexagons (six sides), and regular octagons (eight sides). See Figure 
16-4
.