Page images
PDF
EPUB
[blocks in formation]

FOR TEACHERS.

A Key to New Elementary Geometry has been prepared, and

published for the convenience of teachers, which will be mailed
prepaid, on receipt of 50 cents by the Publishers.

ELEMENTARY GEOMETRY.

BOOK Ι.

GENERAL PRINCIPLES.

PRELIMINARY DEFINITIONS.

1. Geometry is the science of position and extension. The elements of position are direction and distance.

The dimensions of extension are length, breadth, and thick

ness.

2. A Point is that which has position, without magnitude. 3. A Line is that which has length, without either breadth or thickness.

4. A Straight Line is one which

has the same direction in its whole ex

tent; as the line A B.

-B

The word line is frequently used to designate a straight line.

5. A Curved Line is one which

continually changes its direction; as the line CD.

C

D

The word curve is frequently used to designate a curved line.

6. A Surface is that which has length and breadth, without hight or thickness.

7. A Plane Surface, or simply a PLANE, is one in which any two points being taken, the straight line that joins them will lie wholly in the surface.

8. A Curved Surface is one that is not a plane surface, nor made up of plane surfaces.

9. A Solid, or Volume, is that which has length, breadth, and thickness.

[blocks in formation]

tex of the angle, and the lines AB, AC are the sides of the

angle.

An angle may be designated, not only by the letter at its vertex, as C, but when two or more angles have the same vertex, the letter at the vertex always occupies the middle place; as the angle ACD or DCB.

11. Two straight lines are said to be Perpendicular to each other, when their meeting forms equal adjacent angles; thus the lines AB and CD are

perpendicular to each other.

D

A

[blocks in formation]

C

[blocks in formation]

Two adjacent angles, as CAB and BAD, have a common

vertex, as A; and a common side, as A B.

C

[blocks in formation]

E

An Obtuse Angle is one which is greater than a right angle; as the angle EFG.

F

G

Acute and obtuse angles are sometimes called oblique angles.

14. Parallel Lines are such as,

A

B

being in the same plane, cannot meet,

however far either way both of them may be produced; as the lines A B, C D.

[blocks in formation]
[blocks in formation]

of the secant line; as the angles BGH, GHD, and also AGH, GH С.

Alternate Interior Angles lie within the parallels, and on different sides of the secant line, but are not adjacent to each other; as the angles BGH, GHC, and also AGH, GHD.

Opposite Exterior and Interior Angles lie on the same side of the secant line, the one without and the other within the parallels, but not adjacent to each other; as the angles EGB, GHD, and also EGA, GHC, are, respectively, the opposite exterior and interior angles.

PLANE FIGURES.

16. A Plane Figure is a plane terminated on all sides by straight lines or curves.

The boundary of any figure is called its perimeter.

17. A Polygon is a plane bounded by straight lines; as the figure A B C D E. A polygon of three sides is called a E triangle; one of four sides, a quadrilateral; one of five, a pentagon; one of six, a hexagon; one of seven, a heptagon; one of eight, an octagon; one of nine, a nona

[blocks in formation]

gon; one of ten, a decagon; one of eleven, an undecagon; one of twelve, a dodecagon; and so on.

A polygon which has equal sides and equal angles is called a regular polygon; and the equal sides and equal angles are called homologous sides and angles.

A

18. An Equilateral Triangle is one which has its three sides equal; as the triangle A B C.

[blocks in formation]

An Isosceles Triangle is one which has two of its sides equal; as the triangle DEF.

[blocks in formation]

A Scalene Triangle is one which has no two of its sides equal; as the triangle

GHI.

19. A Right-angled Triangle is one which has a right angle; as the triangle JKL.

[blocks in formation]

The side opposite to the right angle is called the hypothenuse; as the side JL.

An Acute-angled Triangle is one which has three acute an

« PreviousContinue »