A Shorter Geometry

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Contents

 FIRST STAGE 1 Direction 11 SECOND STAGE 22 Parallel Straight Lines 29 132 34 Angles of a Polygon 37 Congruent Triangles 49 If two angles of a triangle are equal 56
 PAGE 219 CONSTRUCTION To find the fourth proportional to three 225 CONSTRUCTION On a given straight line to construct 232 AREAS OF SIMILAR FIGURES 237 PARALLEL STRAIGHT LINES 259 ANGLES OF A TRIANGLE A POLYGON 265 If two rightangled triangles have their 272 EXAMINATION PAPERS 278

 Miscellaneous Exercises 60 Drawing to Scale 66 Воок 75 CONTINUOUS CHANGE OF A FIGURE 86 CONSTRUCTION To draw a straight line parallel to a given 95 SYMMETRY 106 PAGE 114 AREA OF TRIANGLE 120 Projections 136 A a+b kak + 143 PRELIMINARY 149 CONSTRUCTION To circumscribe a circle about a given 155 In equal circles or in the same circle 158 Lengths of chords 164 CONSTRUCTION To inscribe a circle in a given triangle 172 ANGLE PROPERTIES 179 E al32 a+ba 187 MISCELLANEOUS EXERCISES 195 AREA OF CIRCLE 202 MISCELLANEOUS EXERCISES 211
 INDEX AND LIST OF DEFINITIONS 297 CHAP PAGE I Planes and Lines 1 1 Parallel positions of Planes and Lines 7 7 Perpendicular positions of Lines and Planes 11 11 Oblique positions of Planes and Lines 16 16 Skew Straight Lines 20 20 Loci 25 25 The Prism 27 27 The Cylinder 33 33 The Pyramid 37 37 The Cone 44 44 The Sphere 48 48 The Solid Angle 60 60 The Regular Solids the Principle of Duality Eulers Theorem 65 65 Coordinates in Space 72 72 Plan and Elevation 75 75 Perspective 89 89 MISCELLANEOUS EXERCISES 93 ANSWERS 105 105 INDEX 107 107

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.