10. Would it be possible to draw a straight line upon a surface that was not plane? If so, give an example.

11. How many arms has an angle?

12. What name is given to the point where the arms meet?

13. When an angle is denoted by three letters, may the letters be

arranged in any order?

14. If not, in how many ways may they be arranged, and what

precaution must be observed?

15. When is it necessary to name an angle

by three letters?

16. How else may an angle be named?
17. OA, OB, OC are three straight lines
which meet at 0. Name the three
angles which they form.

18. Name the angle contained by OA and
OB; by OB and OC; by OC and OA.
19. OA, OB, OC, OD are four straight
lines which meet at 0. Name the
six angles which they form.

20. Name the angle contained by OA and O
OB; by OB and OC; by OC and
OD; by OA and OC; by OB and
OD; by OA and OD.

21. Write down all the ways in which the angle
A can be named.

22. If the arms of one angle are respectively equal to the arms of another angle, what inference can we draw regarding the sizes of the angles?

B

F

23. In the figure to Question 17, if the angles AOB and BOC are added together, what

24. In the same figure, if the angle AOB is taken away from the

angle AOC, what angle is left?

25. In the same figure, if the angle BOC is taken away from the angle AOC, what angle is left?

26. The following questions refer to the figure to Question 19: (a) Add together the angles AOB and BOC; AOB and BOD; AOC and COD; BOC and COD.

(6) From the angle AOD subtract successively the angles COD, AOB, AOC, BOD.

(c) From the angle BOD subtract the angles COD, BOC. (d) To the sum of the angles AOB and BOC add the difference of the angles BOD and BOC; and from the sum of AOB and BOC subtract the difference of BOD and COD.

27. Draw, as well as you can, two equal angles with unequal arms. 28. "1 two unequal equal

29. If two adjacent angles are equal, must they necessarily be right angles? Draw a figure to illustrate your answer.

30. If two adjacent angles are equal, what name could be given to the arm that is common to the two angles?

31. When an angle is greater than a right angle, what is it called?

to say that they never meet though produced indefinitely far either way? Illustrate your answer by reference to the edges of a book, or otherwise.

37. Draw three straight lines, every two of which are parallel. 38. Draw three straight lines, only two of which are parallel.

39. Draw three straight lines, no two of which are parallel.

40. What is the least number of lines that will inclose a space? Illustrate your answer by an example.

41. How many radii of a circle are equal to one diameter ?

42. How do we know that all radii of a circle are equal?

43. Prove that all diameters of a circle are equal.

44. Are all lines drawn from the centre of a circle to the circum

ference equal to one another?

45. What is the distinction between a circle and a circum

ference?

46. Is the one word ever used for the other?

sequences of this supposition are then crammed til e mai

result is reached which is

inferred that the proposition must be the

is called an indirect demonstratica, ir ametime

absurdum (a reducing to the absurd,

SYMBOLS AND ABBREVTANCE

+, read plus, is the sign of addition, i det to
tudes between which is a place and my
-, read minus, is the sign of size 12
magnitude written after a se izda is a
tude written before

~, read difference, is sometimes

not known wichst the magte

the greater.

= is the sign of equality, and agmula diz des map.

which it is placed a

an abbreviation fra a

and 'equal to."

47. How many letters are generally used to denote a circle? 48. Would it be a sufficient definition of a diameter of a circle to say that it consists of two radii?

49. Prove that the distance of a point inside a circle from the centre is less than a radius of the circle.

50. Prove that the distance of a point outside a circle from the centre is greater than a radius of the circle.

51. What is the least number of straight lines that will inclose a

space?

52. What name is given to figures that are contained by straight

lines?

53. Could three straight lines be drawn so that, even if they were produced, they would not inclose a space?

54. What is the least number of sides that a rectilineal figure can

have?

55. ABC is a triangle. Name it in five other

ways.

56. If AB is equal to AC, what is triangle ABC

called?

57. If AB, BC, CA are all equal, what is B

triangle ABC called?

A

58. If AB, BC, CA are all unequal, what is triangle ABC

called?

59. What name is given to the sum of AB, BC, and CA ?

60. Which side of a triangle is called the base?

61. Which side of an isosceles triangle is called the base ?

62. When the hypotenuse of a triangle is mentioned, of what sort must the triangle be?

63. What names are sometimes given to those sides of a rightangled triangle which contain the right angle?

64. Would it be a sufficient definition of an acute-angled triangle to say that it had neither a right nor an obtuse angle?

65. ABC is a triangle. Name by one letter

the angles respectively opposite to

the sides AB, BC, CA.

66. Name by three letters the angles respec

tively opposite to the sides AB, BC, B

CA.

A

67. Name the sides respectively opposite to the angles A, B, C. 68. Name by one letter and by three letters the angle contained by AB and AC; by AB and BC; by AC and BC.