Title 195825392 Textbook Geometry 00 Went Rich 13.2 MB 264
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114 PLANE GEOMETRY. BOOK II.

PROPOSITION XXIX. PROBLEM.

279, To divide a given straight line into equal
parts.

-0

Let AB be the given straight line.

To divide AB into equal parts.
Construction, From A draw the line AO.

Take any convenient length, and apply it to AO as many
times as the line AB is to be divided into parts.

From the last point thus found on AO, as (7, draw CB.

Through the several points of division on AO draw lines
II to CB, and these lines divide AB into equal parts.

Proof. Since AC is divided into equal parts, AB is also, 187
(if three or more \\s intercept equal parts on any transversal, they intercept

equal parts on every transversal).
Q. E. F.

Ex. 101. To divide a line into four equal parts by two different
methods.

Ex. 102. To find a point X in one side of a given triangle and equi
distant from the other two sides.

Ex. 103. Through a given point to draw a line which shall make

equal angles with the two aides of a given angle.

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PROBLEMS. 115

PROPOSITION XXX. PROBLEM.

280, Two sides and the included angle of a trian
gle being given, to construct the triangle.

D
7)

Let the two sides of the triangle be b and c, and the
included angle A.

To construct a A having two sides equal to b and c respec
tively, and the included Z. = /. A.

Construction, Take AB equal to the side c.

At A, the extremity of AB, construct an angle equal to the

given Z A. 276
On^Dtake ACequal to b.

Draw CB.

Then A AGEis the A required.
Q. E. F.

Ex. 104. To construct an angle of 45.

Ex. 105. To find a point X which shall be equidistant from two
given intersecting lines and at a given distance from a given point.

Ex. 106. To draw through two sides of a triangle a line || to the
third side so that the part intercepted between the sides shall have a

given length.

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