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1 THE STRAIGHT LINE 9 1 Angles 9 2 Perpendicular lines . 15 3 Mathematical propositions . ... . 20 4 Polygons and triangles . .... . . 22 5 Isosceles triangles and symmetry . 26 6 Congruence tests for triangles . 30 7 Inequalities in triangles .34 8 Right triangles 1. 9 Segment and angle bisectors . .... . 45 10 Basic construction problems . ...... . 11 Parallel lines. 55 12 The angle sum of a polygon 6 13 Parallelograms and trapezoids 6.. 8 14 Methods of construction and symmetries .... 78 2 THE CIRCLE 83 1 Circles and chords .. . 83 2 Relative positions of a line and a circle . . 89 3 Relative positions of two circles .. . . 92 4 Inscribed and some other angles ..... 97 5 Construction problems . . . 102 6 Inscribed and circumscribed polygons ..... 110 7 Four concurrency points in a triangle . ... 114 3 S1MILARITY 117 . . . . 117 I M ensuration .. . . ... . . . . . .1. . . . . . . .. . . . 117 2 Smilarity of triangles 1... . .. 27 3 Similarity of poly gos . ... ... 34 4 Proponrtionality theorems . 38 S Hom othety . . . .. . . . .. . . . . . . . . . . . . . . 1 3 6 (Geoineti mean . 150 S rigonmiet rc funtions .161 S Applirad ions of algeba, to geometry . .170 9 Coordinates . . . . . . . . . . . . . . . . . . . . . . . 174 4 REGULAR POLYGONS & CIRCUMIFERENCE 183 R egulal polygons . . . . . . . . . . 183 2 Lim its . . . . . . . . . . . . . . . . . . . . . . . . . 195 3 ( ir uinferen e and arc length .1.......... . 99 5 AREAS 209 1 Areas of polygons .... ... ........... 209 2 Several f ulas fr areas of tiagles .. 218 3 reas of similar figures 23 4 A eas of disks and sctr s .22 5 The Pytlagoican thýorem revisited . . . . ... 230