A Shorter Geometry

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Contents

Surface
1
Direction
11
SECOND STAGE
22
PRELIMINARY
28
Parallel Straight Lines
29
Angles of a Polygon
37
Miscellaneous Exercises
60
TABLE OF FACTS OR THEOREMS
75
ANGLES AT A POINT
171
CONSTRUCTION To inscribe a circle in a given triangle
172
ANGLE PROPERTIES
179
If a pair of opposite angles of a quadri
189
MISCELLANEOUS EXERCISES
195
To construct an interior common tangent to two circles
201
MISCELLANEOUS EXERCISES
211
Ratio and proportion
219

To draw the perpendicular bisector of a given straight line
81
PARALLELOGRAMS
87
The locus of a point which is equidistant
101
90
105
MISCELLANEOUS EXERCISES
107
Area by counting squaressquared paper
114
AREA OF TRIANGLE
120
Equivalent triangles which have equal bases
126
THE THEOREM OF PYTHAGORAS
128
Projections
136
MISCELLANEOUS EXERCISES
145
COR A straight line drawn through the midpoint of
153
CONSTRUCTION To inscribe a regular hexagon in a circle
160
THE TANGENT
166
94
225
AH
226
If two triangles have one angle of the
235
i The internal bisector of an angle of
248
If a straight line stands on another straight
257
If straight lines are drawn from a point
264
INEQUALITIES
273
96
293
Drawing to Scale
299
INDEX AND LIST OF DEFINITIONS
307
186
308
101
311
Heights and Distances

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Page xi - In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.
Page ix - The locus of a point which is equidistant from two intersecting straight lines consists of the pair of straight lines which bisect the angles between the two given lines.
Page xvi - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

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