# A Shorter Geometry

CUP Archive

### 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

### 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.