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In describing the properties of a triangle it is not unusual to mark each angular point of the triangle with a letter.

Thus the accompanying triangle is called the triangle A B C, and

the sides are called

A B, B C, and A C,

and the three angles

A

B

are called A, B, C, or the angles C A B, A B C, A CB.

69. Can you make an isosceles triangle without using more than one circle?

When two lines do not meet either way,、 though produced ever so far, they are said to be parallel.'

70. Draw two parallel lines.

71. Can you draw one line parallel to another, and let the two be an inch apart?

72. Can you place two equal sectors so that one corresponding radius of each sector may be in one line, and so that their angles may point the same way?

1 Of course it means two lines in the same plane.

73. Upon the same side of the same line, place two angles that shall be equal to each other, and let each angle face the same way. When two circles have the same centre, they are called concentric circles.

74. Make three concentric circles.

When two circles have not the same centre, and one of them is within the other, they are called eccentric circles.

75. Make two eccentric circles.

76. Draw one line parallel to another line, and let it pass through a given point.

All figures that have four sides take the name of quadrilaterals.'

Of quadrilaterals there are six varieties, consisting of quadrilaterals that have their opposite sides parallel, which are called parallelograms; and quadrilaterals that have not their sides parallel, which are called trapeziums.

Of parallelograms there are four kinds: parallelograms, which have all the sides equal, and all the angles equal, called squares. Paral

1 1 Figures of four sides are also called quadrangles.

lelograms which have the sides equal, but the angles not all equal, called rhombuses. Parallelograms which have all their angles equal, but their sides not all equal, called rectangles; and parallelograms which have neither the sides all equal, nor the angles all equal, called rhomboids.

Of trapeziums there are two kinds : quadrilaterals, that have two only of the sides parallel, called trapezoids; and quadrilaterals that have no two sides parallel, which take the name of trapeziums.

77. Give a sketch of a square, of a rhombus, of a rectangle, of a rhomboid, of a trapezoid, and of a trapezium.

The line that joins the opposite angles of a quadrilateral is called a diagonal.

78. Show that each variety of quadrilateral has two diagonals, and say in which kind the diagonals can be of equal lengths, and in which they cannot

In geometry, one figure is said to be placed in anotner, when the inner figure is wholly

within the outer, and at the same time touches the outer in as many points as the respective forms of the two figures will admit.

79. Describe a circle that shall have a diameter of 11⁄2 inch, and place a square in it.

80. Can you make a rhombus ?

When a rhombus has its obtuse angles twice the size of those which are acute, it is called a regular rhombus.

81. Can you make a regular rhombus?

1

82. Can you make a rectangle? 1

83. Can you make a rhomboid?

84. Can you make a trapezoid?

85. Can you make a trapezium?

When a geometrical figure has more than four sides, it takes the name of polygon, which means many-angled; and when a polygon has all its sides equal, and all its angles equal, it is called a regular polygon.

A polygon that has five sides is called a pentagon.

1 Rectangles are sometimes called oblongs, and sometimes long squares.

A polygon that has six sides is called a hex

agon.

A polygon that has seven sides is called a heptagon.

A polygon that has eight sides is called an octagon.

A polygon that has nine sides is called a

nonagon.

A polygon that has ten sides is called a decagon.

A polygon that has eleven sides is called an undecagon.

A polygon that has twelve sides is called a dodecagon.

You have made a sector with a reëntrant angle.

86. Of how few lines can you make a figure with a reëntrant angle?

87. Of how few sides can you make a figure with two reëntrant angles?

88. Of how few sides can you construct a figure with three reëntrant angles?

89. Show how many equilateral trian

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