42. Can you divide a line into two equal parts?

43. Can you divide an arc into two equal parts?

You have been told that figures bounded by lines are called linear figures.

44. Make a linear figure having the fewest boundaries possible, and in it write its name, and say why such figure claims that name.1

When a figure has for its boundaries three equal lines, it is called an equilateral triangle.2 45. Can you make an equilateral triangle?

46. Can you with three lines make two angles, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen ?

47. Can you so place two equilateral triangles that one side of one of them may coincide with one side of the other?

48. Can you divide an equilateral triangle into two parts that shall be equal to each other and similar to each other?

1 Triangles are also called trilaterals.

2 Equilateral triangles are also called trigons.

49. Can you draw one line perpendicular to another line, from a point that is in the line but not in the middle of it?

The figure formed by two radii and an arc is called a sector.

When a circle is divided into four equal sectors, each of such sectors takes the name of quad

rant.

50. Divide a circle into four equal sectors, and write upon each sector its specific name.

51. Make a set of quadrants, and write in each angle its specific name.

To compare sectors of different magnitudes with each other, geometricians have found it convenient to imagine every circle to be divided into three hundred and sixty equal sectors; and a sector consisting of the three hundred and sixtieth part of a circle, they have called a degree. An arc, therefore, of such a sector is an arc of a degree;' and the angle of such a sector is an angle of a degree.

1 A degree of a circle is concisely marked thus (1°). Thir ty degrees thus (30°). Thirty-five degrees thus (35°).

52. Make a set of quadrants, and write in each angle how many degrees it contains.

All angles greater or less than the angle of a quadrant are called oblique angles.

When an oblique angle is less than a quadrantal angle, that is less than a right angle, that is less than an angle of 90°, it is called an acute angle.

53. Make an acute angle.

When an oblique angle has more degrees in it than 90°, and less than 180°, it is called an obtuse angle.

54. Make an obtuse angle.

55. Make an acute-angled sector.

56. Make an obtuse-angled sector.

When a sector has an arc of 180°, the radii forming with each other one straight line, it has the same claim to be called a sector as it has to be called a segment, and yet it seldom takes the name of either, being generally called a semicircle.

57. Make three sectors, each containing 180°,

aud write in each sector a different name, and yet an appropriate one.

A sector which has an arc greater than a semi-circumference is said to have a reëntrant

angle.

58. Make a reëntrant-angled sector.

59. Say to which class of sectors the degree belongs.

You have halved a line, and you have halved

an arc.

60. Can you divide a segment into two parts. that shall be equal to each other, and similar to each other?

61. Can you divide a sector into two parts that shall be equal to each other, and similar to each other?

It is said by some, the circumference of a circle is 3 times its own diameter; by others, more accurate, that it is 34 times its own diam

eter.

62. Say how you would determine the ratio the circumference of a circle bears to its diam

eter, and say also what you make the ratio to

be.

You have divided a line, an arc, a segment, and a sector, into two equal parts.

63. Can you divide an angle into two equal parts?

When a triangle has two only of its sides of equal length it is called an isosceles triangle.

64. Make an isosceles triangle.

When a triangle has all its sides of different lengths it takes the name of scalene.

65. Make a scalene triangle.

When a triangle has one of its angles a right angle, it is called a right-angled triangle.

66. Make a right-angled triangle.

When a triangle has each of its angles less than a right angle, and all different in size, it is called a common acute-angled triangle.

67. Make a common acute-angled triangle. When a triangle has one of its angles obtuse, it is called an obtuse-angled triangle.

68. Make an obtuse-angled triangle.