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6. A car that cost Mr. Jones $750 was insured against fire in its second year for 60% of its value. What was the premium?

7. A $750 car was insured against theft in its fourth year at 40% of its value. With the rate $2 per $100 of insurance, what was the premium? How much would the insurance company pay if the car were stolen and not found?

Marine Insurance

Marine insurance had to do originally with the insurance of goods while being shipped on board vessels. It has now been extended to include shipments on land as well as at sea. The rates vary with the kind of goods sent, the character of the vessel or other conveyance on which they are shipped, the point to which they are going, etc., so that each case has to be considered more or less as an individual one.

Accident and Health Insurance

Accident insurance provides large cash payments for loss of life or parts of the body as a result of an accident, and also weekly payments in case of disability. One company, for an annual premium of from $20 to $35, according to the occupation of the applicant, will pay $5,000 for the loss of life as a result of an accident or for the loss of both hands or both feet or the sight of both eyes. For total disability, it will pay $25 a week as long as the insured person lives; and for partial disability, $12.50 a week for not more than 26 weeks.

Health insurance guarantees an income when the insured is incapacitated by illness. The premiums depend on the amounts to be paid and also on the age of the insured.

CHAPTER VII

PRACTICAL USES OF GEOMETRY

LINES AND ANGLES

A straight line is a line that does not change its direction. A straight line is drawn by means of a ruler or any straight edge.

A plane is a flat surface, like your desk top or the surface of the blackboard.

Parallel lines are straight lines on the same plane that will never meet, no matter how far they are extended in either direction.

PARALLEL LINES

ANGLE

PERPENDICULAR LINES

Find parallel lines on this book; on your desk; in the schoolroom.

When two lines meet, they form an angle. The angle is the amount of opening between the two lines. The lines are called the sides of the angle.

The meeting point of the lines is the vertex of the angle. When two lines meet so that they make a square corner, like the corner of this page, they form a right angle. Find some right angles in the schoolroom.

Perpendicular lines are straight lines that meet to form a right angle.

ACUTE ANGLE

STRAIGHT ANGLE

OBTUSE ANGLE

An acute angle is an angle less than a right angle.

A straight angle is an angle whose sides extend in opposite directions and form a straight line.

An obtuse angle is an angle larger than a right angle but less than a straight angle.

Estimating and Measuring Distances

The distance between two points is understood to be the straight line distance.

Small distances are measured in inches and parts of an inch. How are larger distances measured? How are very great distances measured?

Many times when a distance has to be obtained only within a foot or two of its correct length, it is "paced off." This is frequently done in measuring land. A man paces off the distance between two points, counting his steps and multiplying their number by the length of one step.

It is a good plan to form the habit of estimating lengths and distances before actually measuring them. After some practice you will find yourself becoming better and better able to judge lengths. This ability will prove of value to you.

When we measure lengths with ordinary tools, we usually get results as accurate as is needed in practice. The degree of accuracy will depend on the care we use in measuring, the

kind of instruments we use, and the distance to be measured. Sometimes two or three persons measure the same distance and an average of the different lengths is taken.

First estimate and then measure

1. The length and the width of a page of this book.

2. The length and the width of your desk.

3. The height of the top of your desk from the floor.

4. The width of one of the schoolroom doors.

5. The width of the blackboard.

6. The length and the width of your schoolroom.

7. Five children may go to the board and each one may draw with a ruler a line of any length. Mark these lines A, B, C, D, E. Now the class may first estimate the lengths of these lines and then measure them.

8. Three or four children may find the length of their steps, by finding what distance they pace off in five steps and dividing this distance by five. Now, knowing the length of one step, each may pace off a distance, such as the length of the schoolroom, the length of the corridor, the length and width of the school lot, etc. Others may check their work by taking actual measurements.

Drawing to a Scale

1. These lines are drawn to the scale 1" 8'. What distance does each line represent?

A

B

C

D

E

2. These three city lots are drawn to the scale 1" = Give the width and the depth of each lot.

[blocks in formation]

40'.

3. Tell the meaning of these scales:

1" = 16', 1, 1" = 40 rd., 8 ft. to the inch. 4. Draw lines 1 inch long, 1 inches long, and 24 inches long. If the scale is, what distances do these lines represent?

5. The scale is 40 rd. to the inch. Draw a rectangle 2 inches by 3 inches. This is the plan of Mr. Johnson's farm. Find the length and the width of the farm. 6. If the scale is 1" = 16', draw lines to represent 16 ft. 50 ft.

8 ft.

20 ft.

42 ft.

7. A map is drawn on a scale of 100 miles to 1 inch. What distances are represented by 3 inches? 1 inches? 4 inches? 2 inches?

8. On the above map what will represent 600 miles? 50 miles? 250 miles? 425 miles? 1,000 miles?

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