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Of Lines.

5. Lines which are perpendicular to the horizon, or to the water level, are called vertical lines. Thus, trees and plants grow vertically, or in lines perpendicular to the horizon.

6. If two parallel lines CD, AB, are cut by a third line IG, the angles A

-B IHD and AFG, are called alternate C

-D

H angles. These angles are equal to G each other. The angle IHD is also equal to the angle IFB, and to the opposite angle CHG.

7. If a line be perpendicular to one of several parallel lines, it will

A

-B be perpendicular to all the oth

-D ers. Thus, if AB, CD and EF, be

E E

F parallel, the line CH drawn perpendicular to AB, will also be perpendicular to CD and EF.

H

QUEST.-5. What are vertical lines? Are the corners of a house vertical? Point out the lines of a window which are horizontal. Point out those which are vertical. Point out the lines of a room which are horizontal: also those which are vertical. 6. If two parallel lines are cut by a third line, point out the alternate angles. Are these angles equal or unequal ? Name all the angles which are equal to each other. 7. If several lines are parallel, and a line be drawn perpendicular to one of them, will it be perpendicular to all the others ?

Of Plane Figures.

8. From the same point D, only

D
one line DB, can be drawn, which
shall be perpendicular to AB.

A B C
If oblique lines be drawn, as DC,
DF, then:

1st.—The perpendicular DB, will be shorter than any of the oblique lines.

2nd.—The oblique lines which are nearest the perpendicular, will be less than those which are more remote.

SECTION IV.

OF PLANE FIGURES.

1. A plane figure is a portion of a plane, terminated on all sides by lines, either straight or curved.

If the lines are straight, the space they enclose is called a rectilineal figure, or polygon. The lines themselves, taken together, are called the perimeter of the polygon. Hence, the perimeter of a polygon is the sum of all its sides.

QUEST.-8. From the same point, how many perpendiculars can be drawn to a line? If oblique lines be drawn, which will be the least? Which the greatest ? 1. What is a plane figure ? If the lines are straight, what is the plane figure called? What is the sum of the lines called ?

Of Plane Figures.

2. A polygon of three sides, is called a triangle.

3. A polygon of four sides, is called a quadrilateral.

4. A polygon of five sides, is called a pentagon.

5 A polygon of six sides, is called a hexagon.

6. A polygon of seven sides, is called a heptagon.

7. A polygon of eight sides, is called an octagon.

S. A polygon of nine sides, is called a nonagon.

QUEST.-2. What is a polygon of three sides called ? 3. What is a po lygon of four sides called? 4. What is a polygon of five sides called ? 5. What is a polygon of six sides called ? 6. What is a polygon of seven sides called ? 7. A polygon of eight sides ? 8. A polygon of nine sides?

Of Plane Figures.

9. A polygon of ten sides, is called a decagon.

10. A polygon of twelve sides is called a dodecagon.

11. Three straight lines, are the smallest number which can enclose a space.

12. There are several kinds of triangles.

First.An equilateral triangle, which has its three sides all equal.

Second.-An isosceles triangle, which has two of its sides equal.

QUEST.-9. What is a polygon of ten sides called ? 10 Of twelve sides ? Make each of the polygons on the board. 11. What is the smallest number of straight lines which can enclose a space ? 12. When is a triangle equilateral ? When is a triangle isosceles ?

Of Plane Figures.

Third.--A scalene triangle, which has its three sides all unequal.

Fourth.---A right angled triangle, which has one right angle. In the right angled triangle BAC, the side BC opposite the right angle, is called the hypothenuse.

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13. The base of a triangle is the side on which it stands. Thus, BA is the base of the right angled triangle BAC. The line drawn from the opposite angle perpendicular to the base, is called the altitude. Thus, AC is the altitude.

14. There are several kinds of quadrilaterals.

First. The square, which has all its sides equal, and all its angles right angles.

Quest.-What is a scalene triangle? What is a right angled triangle ? What is the side opposite the right angle called ? 13. What is the base of a triangle? What is the altitude of a triangle? Make on the board the different kinds of triangles. 14. What is a square ?

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