# A Shorter Geometry

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### Contents

 FIRST STAGE 1 Direction 11 SECOND STAGE 22 Parallel Straight Lines 29 Angles of a Polygon 37 130 39 257 42 Congruent Triangles 49
 ARCS ANGLES CHORDS 156 1 equal chords are equidistant from the centres 163 CONSTRUCTION To draw the tangent to a circle at a given 169 If two circles touch the point of contact lies 175 If a straight line touch a circle and from 193 AREA OF CIRCLE 202 MISCELLANEOUS EXERCISES 211 PAGE 219

 If two angles of a triangle are equal 56 Miscellaneous Exercises 60 Drawing to Scale 66 Воок 75 CONTINUOUS CHANGE OF A FIGURE 86 SUBDIVISION OF A STRAIGHT LINE 96 SYMMETRY 106 Area by counting squaressquared paper 114 AREA OF TRIANGLE 120 Projections 136 MISCELLANEOUS EXERCISES 142 PRELIMINARY 149
 CONSTRUCTION To find the fourth proportional to three 225 If in two triangles ABC DEF 230 CONSTRUCTION On a given straight line to construct 232 AREAS OF SIMILAR FIGURES 237 ii If AB CD two chords of a circle 243 ii The external bisector of an angle of 249 lines 262 Straight lines which are parallel to the same 263 If two rightangled triangles have their 272 REVISION PAPERS 278 INDEX AND LIST OF DEFINITIONS 307

### 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.