Idiot\'s Guides Basic Math and Pre-Algebra

154 Part 3: The Shape of the World

In the angle ’XYZ, the vertex is Y, and the sides are rays YX and YZ. You can name angles by

three letters, one on one side, the vertex, and one on the other side. ’XYZ and ’ZYX are both

names for this angle. An angle can be named by just its vertex, for example, ’Y, as long as it is

the only angle with that vertex.

X

Z

Y

CHECK POINT

Draw and label each figure described.

1. Line segment PQ


2. Ray YZ


3. Angle ’DEF
   4. Rays AB and AC
   5. Angles ’PQR and ’RQT

Length and Angle Measure

Well, you found things you can measure: a line segment or an angle. They don’t go on forever.

You can measure them and actually stop somewhere. So how do you do it?

Measuring just means assigning a number to something to give an indication of its size. The

number depends on the ruler you’re using. Feet? Inches? Centimeters? Furlongs? They all

measure length (although you don’t see furlongs used much outside of horse racing).

A ruler is just a line or line segment that you’ve broken up into smaller segments, all the same

size, and numbered. You could even use a number line, and many times we will.

If you place a ruler next to a line segment, each endpoint of the segment will line up with some

number on the ruler (even if it’s one of the little fraction lines in between the whole numbers).

The numbers that correspond to the endpoints are called coordinates, and the length of the line

segment is the difference between the coordinates. Technically, the length is the absolute value

of the difference, because direction doesn’t matter.

DEFINITION

A ruler is a line or segment divided into sections of equal size, labeled with numbers,

called coordinates, used to measure the length of a line segment.