# A Shorter Geometry

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### Contents

 FIRST STAGE 1 Direction 11 SECOND STAGE 22 Parallel Straight Lines 29 Angles of a Polygon 37 Congruent Triangles 49 Miscellaneous Exercises 60 Drawing to Scale 66
 CONSTRUCTION To inscribe a circle in a given triangle 172 79 178 ANGLE PROPERTIES 179 SECTION IX 187 If a straight line touch a circle and from 193 MISCELLANEOUS EXERCISES 199 FURTHER EXAMPLES OF LOCI 205 Ratio and proportion 219

 BOOK I 75 To draw a straight line perpendicular to a given straight 83 If one pair of adjacent sides of a parallelogram 89 Area by counting squaressquared paper 90 3 A quadrilateral is a parallelogram if both pairs 93 AREA OF PARALLELOGRAM 117 CONSTRUCTION To construct a triangle equivalent to 124 THE THEOREM OF PYTHAGORAS 128 Projections 136 118 140 A a+b kak+bk 142 PRELIMINARY 149 CONSTRUCTION To circumscribe a circle about a given 155 CONSTRUCTION To inscribe a regular hexagon in a circle 160 THE TANGENT 166
 883 224 94 225 CONSTRUCTION On a given straight line to construct 232 257 237 RECTANGLE PROPERTIES 240 261 243 121 246 ANGLES OF A TRIANGLE A POLYGON 265 INEQUALITIES 273 96 293 188850 307 233 308 126 310 101 311

### Popular passages

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.