# 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 circumscribe a circle about a given 155 The Tangent 166 Angles at a point 171 Construction To inscribe a circle in a given triangle 172 Angle properties 179 Miscellaneous exercises 195 Area of circle 202 Miscellaneous exercises 211

 Table of facts or theorems 75 Continuous change of a figure 86 Construction To draw a straight line parallel to a given 95 The locus of a point which is equidistant 102 Area by counting squaressquared paper 114 Area op triangle 120 The theorem op Pythagoras 128 Projections 136 A a + bk ak + bk 142 PAGE 149
 Ratio and proportion 219 If H K are points in the sides AB AC of 226 Proportional compasses 236 ii If AB CD two chords of a circle 243 ii The external bisector of an angle of 249 If a straight line stands on another straight 257 those straight lines is equal or supplementary to 264 Inequalities 273 Index and List of Definitions 307

### 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 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.
Page xviii - 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.