FIG. 1

A boy who plans to make a radio set, a footstool, a kite, or a canoe must determine by measurement the amount of material he needs. A girl who is going to make an apron, a doily, a tablecloth, or a dress determines by measurement the required amount of material before buying it. She knows from experience that failure to measure may cause waste of material and money if she should purchase more than she needs.

In making a cake it is safer to use a measuring cup and scale than to guess at the amount of the ingredients. When we are sick, the doctor measures our temperature with a thermometer. We use clocks to measure the time, a gas meter to tell the amount of gas we use, a speedometer to show how fast our car travels, and a steam gage to determine the pressure in our heating plant.

The accuracy required in measurement depends largely on the use to be made of the result. If a boy wants to measure the length of the block in which he lives, he may determine it by simply stepping it off; but the surveyor needs to measure the block with great care using as an instrument of measurement—a well-made steel tape. A carpenter can measure sufficiently well with a yardstick or tapeline, but the

machinist finds it necessary to use a vernier caliper (Fig. 2) and a micrometer (Fig. 3) to measure a required length.

EXERCISES

1. Make a list of the measuring instruments used in your household, and tell how each is used.

2. If you are studying science, make a list of the measuring instruments used in that course and tell what they are used for.

3. Name some measuring instruments that are used in stores, offices, and factories.

2. The meaning of a straight line. We shall begin measuring by finding lengths of straight-line distances, because lengths laid off on straight lines are very simple to measure. A very good idea of what is ordinarily called a straight line may be obtained from the following:

Fold a sheet of paper and crease it by moving a finger along the fold. The crease of the paper represents a straight line. Boundary lines are frequently straight lines. Thus, the edge of a good ruler, the edges of a sheet of notebook paper, and the boundaries of a window pane are examples of straight lines. When we study lines in geometry we do not consider width, thickness, color, or weight. Geometric lines have only length, and we are interested mainly in measuring lengths.

EXERCISES

1. Point out illustrations of straight lines in the classroom.

2. State some examples of straight lines found outside of the classroom.

3. Can you mention some examples of straight lines found in nature?

3. How to make drawings representing straight lines. Various instruments may be used to make drawings representing straight lines. Fig. 4 is a picture of a ruler. The edge AB is a straight line.

A

B

21

3

FIG. 4

If the marks or graduations are omitted from a ruler, it is called a straightedge (Fig. 5).

0

FIG. 6

FIG. 5

Other instruments used to draw straight lines are the triangle (Fig. 6) and the Tsquare (Fig. 7).

We shall now learn how to use the ruler in drawing straight lines.

FIG. 7

EXERCISES

1. Place a ruler on a sheet of paper (Fig. 8) and move the point of a sharp pencil along the edge making a line on the paper. The drawing obtained is said to represent a straight line. To be brief, we shall call it a straight line, but strictly speaking, it is

not a geometrical line because it has width.

FIG. 8

2. The drawings (Fig. 9) are formed by straight lines. Study

Square

Parallelogram

Rectangle

Triangle

FIG. 9

the shapes and remember the names. Then, without looking at the figures, draw others like them on a sheet of notebook paper.

Find other figures of such shapes in the classroom.

3. Make drawings like those shown in Fig. 10.

FIG. 10

4. By means of a ruler or straightedge, test whether or not a surface is plane (flat).

Suggestion: Place the straight edge of the ruler on the surface in a number of positions (Fig. 11). If for every possible position the edge lies completely on the surface, the latter is said to be plane. Apply this test to your desk; to a table top. A carpenter when making a plane surface uses this method of testing.

4. Points. Small dots made on paper with a sharp

1. Draw two intersecting (crossing) straight lines. From the figure tell how many times two straight lines can intersect.

This exercise illustrates the fact that two straight lines can have only one point in common. The point in which two straight lines intersect is their point of intersection.

2. Draw four straight lines passing through a fixed point A. How many straight lines may be drawn through A?

This exercise illustrates the fact that through a given point any number of straight lines may be drawn.