Ex. 8. Repeat Ex. 6, for fig. 5, (i) using inches, (ii) using centimetres.

X
A

fig. 5.

X

B

Ex. 9. Measure in inches, and also in centimetres, the length of the paper you are using.

Your ruler is probably too short to measure directly; divide the length into two (or more) parts by making a pencil mark on the edge, and add these lengths together.

Ex. 10. Measure the breadth of your paper in inches and also in centimetres.

Ex. 11. Draw a straight line about 6 in. long and cut off a part AB=2 in., a part BC=1·5 in., and a part CD = 1.8 in.; find the length of AD by adding these lengths; check by measuring AD. [Make a table as in Ex. 3.]

Ex. 12.

Repeat Ex. 11, with

BC= .5 cm.,

CD = 2.4 cm.

AB = 1.8 in., BC = 2.9 in.,

CD = .6 in.

(v) Ex. 13. A man walks 3.2 miles due north and then 1.5 miles due south, how far is he from his starting point? Draw a plan (1 mile being represented by 1 inch) and find the distance by

measurement.

Ex. 14. A man walks 5.4 miles due west and then 8.2 miles due east, how far is he from his starting point? (Represent 1 mile by 1 centimetre.)

Ex. 15. A man walks 7.3 miles due south, then 12.7 miles due north, then 1.1 miles due south, how far is he from his starting point? (Represent 1 mile by 1 centimetre.)

Ex. 16. Draw a straight line, guess its middle point and mark it by a short cross-line; test your guess by measuring the two parts.

Ex. 17. Repeat Ex. 16, three or four times with lines of various lengths. Show by a table how far you are wrong.

Ex. 18. Draw a straight line of 10.6 cm.; bisect it by calculating the length of half the line and measuring off that length from one end of the line, then measure the remaining part.

+

When told to draw a line of some given length, you should draw a line a little too long and cut off a part equal to the given length as in fig. 6. You should also write the length of the line against it, being careful to state the unit.

Ex. 19.

in Ex. 18.

Ex. 20. in Ex. 18.

1.3 in.

fig. 6.

Draw a straight line 3-2 in. long, bisect it as

Draw a straight line 2-7 in. long, bisect it as

Ex. 21. Draw straight lines of the following lengths, bisect each of them: (i) 7·6 cm., (ii) 10·5 cm., (iii) 4·1 in., (iv) ·9 in., (v) 5.8 cm., (vi) 11·3 cm.

A good practical method of bisecting a straight line (AB) is as follows-measure off with dividers equal lengths (AC, BD) from each end of the line (these lengths should be very nearly half the length of the line) and bisect the remaining portion (CD) by eye.

Ex. 22. Draw three or four straight lines and bisect them with your dividers (as explained above); verify by measuring each part of the line (remember to write its length against each part).

Ex. 23. Open your dividers 1 cm., apply them to the inch scale and so find the number of inches in 1 centimetre.

Ex. 24. Find the number of inches in 10 cm. as in Ex. 23; hence express 1 cm. in inches. Arrange your results in tabular

form.

Ex. 25. Find the number of centimetres in 5 in. as in Ex. 23; hence find the number of centimetres in 1 inch.

a

d

b

e

Ex. 26.

h

k fig. 8.

Guess the lengths of the lines in fig. 8 (i) in inches, (ii) in centimetres; verify by measurement. Make a

table thus:

to form an angle at O. O is called the vertex of the angle, and OA, OB its arms.

An angle may be denoted by three letters; thus we speak of the angle AOB, the middle letter denoting the vertex of the angle and the outside letters denoting points on its arms.

If there is only one angle at a point O, we call it the angle O.

Sometimes an angle is denoted by a small letter placed in it; thus in the figure we have two angles a and b.

▲ is the abbreviation for angle.

a

fig. 11.

Two angles AOB, CXD (see figs. 10 and 12), are said to be equal when they can be made to fit on one another exactly (i.e. when they are such that, if CXD be cut D

out and placed so that X is on O and XC along OA, then XD is along OB). It is important to notice that it is not necessary for the arms of the one angle to be equal to those of the other, in fact the size of an angle does not depend on the lengths of its

arms.

Ex. 27. Draw an angle on your paper and dividers to the same angle.

fig. 12.

open your

Ex. 28. Which is the greater angle in fig. 13 Test by making on tracing paper an angle equal to one of the angles and fitting the trace on the other.

Ex. 29. Name the angle at O in fig. 14 in as many different

ways as you can.

Ex. 30. Take a piece of paper and fold it, you will get something like fig. 15, fold

it again so that the edge OB fits on the edge OA; now open the paper; you have four angles made by the creases, as in fig. 16; they are all equal for when folded they fitted on one another. Such angles are called right angles. An angle less than a right angle is called an acute angle. An angle greater than a right angle is called an obtuse angle.

Ex. 31. Make a right angle BOC as in Ex. 30, cut it out and fold so that OB falls on OC. Does the crease

(OE) bisect BOC? (i.e. are

LS BOE, EOC equal?) What

fraction of a right angle is each of the 4s BOE, EOC?

B