# A Shorter Geometry

CUP Archive

### Contents

 Surface 1 Direction 11 SECOND STAGE 22 Area by counting squaressquared paper 23 Parallel Straight Lines 29 More exact measurement by estimation 40 Congruent Triangles 49 Miscellaneous Exercises 60
 MISCELLANEOUS EXERCISES 195 AREA OF CIRCLE 202 MISCELLANEOUS EXERCISES 211 Ratio and proportion 219 CONSTRUCTION To find the fourth proportional to three 225 CONSTRUCTION On a given straight line to construct 232 AREAS OF SIMILAR FIGURES 237 ii If AB CD two chords of a circle 243

 Book I 75 CONTINUOUS CHANGE OF A FIGURE 86 LOCI 96 The locus of a point which is equidistant 102 AREA OF PARALLELOGRAM 117 To construct a triangle equivalent to 124 THE THEOREM OF PYTHAGORAS 128 Projections 136 MISCELLANEOUS EXERCISES 145 PRELIMINARY 149 CONSTRUCTION To circumscribe a circle about a given 155 CONSTRUCTION To inscribe a regular hexagon in a circle 160 THE TANGENT 166 ANGLES AT A POINT 171 CONSTRUCTION To inscribe a circle in a given triangle 172 ANGLE PROPERTIES 179 equal 183 93 188 If a pair of opposite angles of a quadri 189
 ii The external bisector of an angle of 249 If a straight line stands on another straight 257 ANGLES OF A TRIANGLE A POLYGON 265 INEQUALITIES 273 INDEX AND LIST OF DEFINITIONS 297 CHAP 1 IV 16 79 19 94 22 VI 25 The Cylinder 33 XI 48 XII 60 Coordinates in Space 72 85 85 Perspective 89 ANSWERS 105 A theorem and its converse 109

### Popular passages

Page xiii - 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 xxi - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Page xi - 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.