A School Geometry |
Contents
CONTENTS PART | 1 |
SECT PAGE 1 Revision of Fundamental Ideas | 3 |
Kinds of triangles | 6 |
Parallel lines | 7 |
Isosceles triangles | 11 |
Congruent triangles | 16 |
Parallelograms | 27 |
Formal Constructions and Drawing Exercises | 38 |
Some important examples | 122 |
Angles in segments cyclic quadrilaterals | 124 |
Inequalities | 134 |
Tangents to circles | 145 |
Equal arcs and equal chords | 159 |
The alternate segment | 168 |
Tests for concyclic points | 176 |
Constructions | 188 |
Angles of polygons | 55 |
Intercepts | 58 |
Images | 65 |
Parallel lines and planes | 67 |
Revision Papers IXX | 70 |
Equivalent figures and areas | 74 |
The measurement of areas | 80 |
The Theorem of Pythagoras | 87 |
Perpendicular lines and planes | 92 |
Further applications of the Theorem of Pythagoras | 96 |
Construction of a rectangle equivalent to a polygon | 99 |
Notes on theoretical constructions | 102 |
Examples in dissection | 106 |
Rational rightangled triangles | 107 |
Incommensurable magnitudes and irrational numbers | 108 |
Historical Note | 110 |
Mensuration | 111 |
PART II | 113 |
The common tangents to two circles | 192 |
A recent theorem | 198 |
Revision Papers XXIXLVI LVI | 199 |
PART III | 209 |
Rectangle properties of a circle | 220 |
Geometrical illustrations of algebraical identities | 231 |
Use of similar triangles | 235 |
The fundamental theorems on congruence and parallels | 247 |
Discussion of Theorem 44 | 262 |
The classical proof by the method of superposition | 264 |
Similar triangles The fundamental theorems | 265 |
Harder theorems on proportion | 270 |
Medial section and the regular pentagon | 279 |
An illustration of the use of Algebra | 282 |
Geometric solution of quadratic equations | 283 |
Conclusion of this Part A challenge exercise | 284 |
ANSWERS | 289 |
293 | |
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Common terms and phrases
AB² ABC cut ABCD AC² altitudes AÔB Assumption BÂC base BC² bisector of angle bisects centre circle ABC circles cut circles touch circumcircle collinear common tangent congruent triangles const Construction cut the circle cut the line cuts AC cyclic quadrilateral diagonals diameter distance draw a circle Draw a triangle equilateral triangle equivalent EXERCISE Find the length Geometry given circle given line given point incentre inscribed interval isosceles trapezium isosceles triangle line cuts locus mid-point of side opposite sides parallel Axiom parallel lines parallelogram perpendicular plane polygon produced Proof Prove Pythagoras quadrilateral ABCD radii radius rect rectangle rhombus right angles right bisector segment semiperimeter side BC similar triangles square subtended tangent THEOREM trapezium triangle ABC