1. Angles are measured by a protractor. The center O is placed

gree contains 60 minutes (60′), and every minute contains 60 seconds (60").

3. Draw angles of 90°; of 45°; of 60°; of 120°; of 105°.

4. Which of these are acute?

Which obtuse?

Measure them.

The Six Quadrilaterals

1. A figure bounded by four straight lines is a quadrilateral (quattuor four, latus a side).

2. There are three classes of quadrilaterals, namely, (a) those with opposite sides parallel; (b) with one pair of sides parallel; (c) with no two sides parallel.

A

B

D

3. A figure in which the opposite sides are parallel is a parallelogram. Are A, B, C, and D parallelograms?

4. Describe A as to sides and as to angles.

5. A figure whose sides are equal and whose angles are right angles is a square.

6. Describe B as to sides and angles.

7. A parallelogram whose angles are right is a rectangle.

8. Is A a rectangle? Is B?

Is B a square?

A square may be said to be an equilateral rectangle.

9. Describe C as to sides; as to angles.

10. A parallelogram whose sides are equal, but whose angles are not right angles, is a rhombus.

11. Describe D as to sides; as to angles.

12. A parallelogram whose angles are not right angles is a rhomboid. Is C a rhomboid?

A rhombus might be called an equilateral rhomboid.

NOTE. One generally speaks of a figure like D as a parallelogram, and gives to any of the other three special parallelograms its proper name, as square, rectangle, or rhombus.

A

D

13. Which of the parallelograms are equilateral? Equiangular ? 14. Any side upon which the parallelogram is supposed to stand is its base. That which shows the height of a parallelogram is its altitude.

In the figure BC is the base and AE the altitude.

BE

C

15. The altitude and base are always perpendicular to each other. 16. The straight line AC joining the vertices of opposite angles is a diagonal. What other diagonal has the parallelogram ABCD? 17. By cutting, compare the two figures into which a diagonal divides a parallelogram.

18. Prove by cutting accurately from cardboard that

(1) A diagonal bisects a parallelogram.

(2) The opposite angles of a parallelogram are equal.

19. Prove by measuring with a protractor that—

The sum of the angles of any quadrilateral is equal to 360 degrees, or four right angles.

20. A quadrilateral having but one pair of sides parallel, as in Fig. E, is a trapezoid.

21. If no two of the sides of a quadrilateral are parallel, the figure is a trapezium.

The Measurement of Rectangles

1. A rectangle 1 in. wide and 5 in. long contains how many square inches? (See figure.)

2. A rectangle 4 in. wide and 5 in. long will contain how many rectangles 1 in. by 5 in. ?

3. How many square inches in a rectangle 4 in. wide and 5 in. long?

4. What is the area of a rectangle 8 in.

wide and 15 in. long?

A

5 in.

4 in.

5. A rectangle a foot wide and 20 ft. long contains how many square feet? rectangle 12 times as wide and the same length will contain 12 x

sq. ft.

6. Find the area of a rectangle 15 ft. long and 7 ft. wide.

7. Find the area of a rectangle 8 ft. by 15 ft.

8. Find the area of a square rod in square feet; in square yards. 9. A piece of land measures 20 rods one way and 25 rods the other. Find its area in square rods; in acres.

10. A kindergarten table 4 ft. 3 in. long and 20 in. wide is marked off in square inches. How many are there?

11. In a flag 10

feet long and as wide how many square yards of bunting, not allowing for seams?

12. A patchwork quilt 3 yards square is made of 4-inch silk squares. How many are there ?

SUGGESTION. How many squares in a strip 1 square wide and 3 yards long? How many such strips in the quilt?

13. What is the area of mile of street 4 rods wide?

14. A lot of land 56 ft. by 125 ft. is sold at 49 a square foot. Required the proceeds of the sale.

15. A swimming tank is 40 ft. long and 18 ft. wide. What will it cost to cement the bottom at $2.25 per square yard?

16. A city block is 600 ft. long and as wide. How many acres does it cover?

17. A half a mile of 60-ft. street is paved with granite blocks. How many will be required at the rate of 36 to a square yard?

18. What will a sheet of zinc 8 feet long and 32 inches wide cost at 7 a pound if every square foot weighs 8 ounces?

19. Estimate the cost of the blackboards in your schoolroom at 75¢ a square yard.

20. What shall I pay Mr. Bates for concreting a wall 60 ft. long, 4 ft. wide half the length, and 3 ft. wide the rest of the way? The price is 75 a square yard.

21. If a city lot containing 3750 square feet has a frontage of 50 feet, how deep is it?

1. Ingrain carpets are generally woven in strips 1 yd. wide; other carpets yd. What two advantages come from running the strips lengthwise of the floor rather than across it?

2. On floors of the following widths, which of the two widths (1 yd. and & yd.) could be used without cutting or turning under any strip?

12 ft. 15 ft. 221 ft. 27 ft. 13 ft.

20 ft. 18 ft. 3. How many strips of ingrain carpet are needed to carpet a room 18 ft. square? How many yards in each strip? In all, if there is no waste in matching?

4. How many strips of brussels or tapestry are needed for a room 15 ft. by 21 ft.? How many running yards in each strip? How many in all, if there is no waste in matching? Find the cost at $1.25 per yard.

5. How many strips of ingrain will be needed to carpet a room 14 ft. by 20 ft., the strips to run lengthwise, no strip to be cut? How many yards in all, if there is no waste in matching?

6. On the same conditions, what will brusselsyd. wide cost at $1.50 per yard?

7. What will 4-foot oilcloth cost for the same room at $1? In this case, would it be cheaper to put the strips crosswise? Why?

Find the cost of carpeting floors under the following conditions (strips that are cut cost as if whole):·