Causes

North.

.40 .49 2.08 1.59 .23 .05 .52

$5.14

5.36

.40 .492.08 1.59 .23 .05 .44 .06 .07 5.41 .40.492.081.59

6. The table below states some reasons why children leave the public schools. Represent the facts by a circle graph.

Leaving city...

Going to work.

Poor health.

Staying at home.

Going to private school.

Various other causes...

7. A street car company gave wide publicity to the following

statement:

Number of Pupils

Withdrawn

1,153

284

195

121

84

41

Represent these facts by means of a circular graph.

Total

8. In a family one of the daughters keeps a careful account of all expenditures. At the end of the year she finds that she has used $1078.23 of her parents' money. This amount was distributed as follows:

9. Find illustrations of circular graphs in books on science, geography, business, cooking, and other subjects. Look for uses of circular graphs in newspapers and magazines. Then write a paper on circular graphs.

120. What all pupils should know and be able to do. Having studied Chapter VI every pupil should be able:

1. To copy simple designs using only ruler and compass, as shown in §102; to draw an equilateral triangle;

2. To use correctly the terms: local time, standard time, latitude, longitude, time belt, and circle;

3. To change longitude to local time;

4. To read gas and electric-light meters;

5. To make circular graphs;

The following theorems should be known:

1. Equal circles have equal radii.

2. Equal central angles have (intercept) equal arcs. 3. Circles having equal radii are equal.

4. Equal arcs have (are intercepted by) equal central angles.

5. A central angle is measured by the intercepted arc.

121. Typical problems and exercises. Give answers and solutions for the following questions and problems:

1. Explain how you read a gas meter. Illustrate your statement with a drawing, showing a reading of 54,800 cubic feet.

2. How are places on the surface of the earth located by means of latitude and longitude? On a drawing locate the position of a place whose latitude is 54° 42′ S., and whose longitude is 76° 30′ W.

3. What is the relation of local time to longitude? When it is 1 P.M. in Denver, what is the corresponding local time of a place 32° east of Denver?

4. How is the difference in local time for two cities found from the longitudes?

5. A store sells $83,000 worth of goods in the year, the cost of which was $52,000. The expenses amounted to $12,000. Make a circular graph showing cost, expenses, profits, and total sales.

6. Write a paper on one of the following topics:

a. Designs made by means of circles.

b. Uses of the circle.

c. Time.

d. Daylight saving.

CHAPTER VII

GEOMETRIC CONSTRUCTIONS.
MEASUREMENT OF THE CIRCLE

THE USE OF THE CIRCLE IN MAKING
CONSTRUCTIONS

122. Geometric constructions. The constructions in this chapter are to be made by using only compass and straightedge. Such constructions are called geometric constructions. The graduated ruler and the protractor may be used as checking instruments after the construction is made.

123. Construction of a triangle whose sides are given. One of the most useful applications of the circle is the construction of geometrical figures. A simple construction is the drawing of a triangle whose sides are to be of given lengths (Exercise 13, §102). This construction is made as follows:

Draw a triangle, as ABC (Fig. 231).

Draw A,D>AB, and with the compass lay off A,B1 on A1D making A1B1= AB.

With radius AC and A, as center, draw an arc at C1. With radius BC and B, as center, draw a second arc intersecting the first at C1.

Draw A1C, and B1C1.

Cut

1

1

A,B,C, from the paper and place it on ABC. If your construction is well done it will be possible to make the two triangles coincide.

This exercise illustrates the following principle: When two triangles have the corresponding sides equal they are congruent.

The principle just established means that all triangles having their corresponding sides equal are really the same triangle in different positions, and cannot be different in size or in shape. This is the reason why triangles are used in the construction of objects that are to stay rigid, such as trusses, brackets, etc. (Fig. 232).

FIG. 232