Basic Mathematics for Economists

Contents......Page 10
1.2 Undefined Terms of Geometry: Point, Line, and Plane......Page 12
1.3 Line Segments......Page 13
1.4 Circles......Page 14
1.5 Angles......Page 15
1.6 Triangles......Page 20
1.7 Pairs of Angles......Page 23
2.1 Proof By Deductive Reasoning......Page 29
2.2 Postulates (Assumptions)......Page 31
2.3 Basic Angle Theorems......Page 36
2.4 Determining the Hypothesis and Conclusion......Page 38
2.5 Proving a Theorem......Page 40
3.1 Congruent Triangles......Page 45
3.2 Isosceles and Equilateral Triangles......Page 50
4.1 Parallel Lines......Page 59
4.2 Distances......Page 66
4.3 Sum of the Measures of the Angles of a Triangle......Page 70
4.4 Sum of the Measures of the Angles of a Polygon......Page 75
4.5 Two New Congruency Theorems......Page 79
5.1 Trapezoids......Page 88
5.2 Parallelograms......Page 90
5.3 Special Parallelograms: Rectangle, Rhombus, and Square......Page 93
5.4 Three or More Parallels; Medians and Midpoints......Page 96
6.1 The Circle; Circle Relationships......Page 104
6.2 Tangents......Page 110
6.3 Measurement of Angles and Arcs in a Circle......Page 114
7.1 Ratios......Page 132
7.2 Proportions......Page 133
7.3 Proportional Segments......Page 136
7.4 Similar Triangles......Page 139
7.5 Extending A Basic Proportion Principle......Page 144
7.7 Segments Intersecting Inside and Outside a Circle......Page 146
7.8 Mean Proportionals in a Right Triangle......Page 148
7.9 Pythagorean Theorem......Page 149
7.10 Special Right Triangles......Page 151
8.1 Trigonometric Ratios......Page 165
8.2 Angles of Elevation and Depression......Page 169
9.1 Area of a Rectangle and of a Square......Page 175
9.2 Area of a Parallelogram......Page 176
9.3 Area of a Triangle......Page 177
9.4 Area of a Trapezoid......Page 178
9.5 Area of a Rhombus......Page 179
9.6 Polygons of the Same Size or Shape......Page 180
9.7 Comparing Areas of Similar Polygons......Page 182
10.1 Regular Polygons......Page 190
10.2 Relationships of Segments in Regular Polygons of 3, 4, and 6 Sides......Page 192
10.3 Area of a Regular Polygon......Page 193
10.4 Ratios of Segments and Areas of Regular Polygons......Page 194
10.5 Circumference and Area of a Circle......Page 195
10.6 Length of an Arc; Area of a Sector and a Segment......Page 196
10.7 Areas of Combination Figures......Page 199
11.1 Determining a Locus......Page 206
11.2 Locating Points by Means of Intersecting Loci......Page 209
11.3 Proving a Locus......Page 210
12.1 Graphs......Page 214
12.2 Midpoint of a Segment......Page 216
12.3 Distance Between Two Points......Page 217
12.4 Slope of a Line......Page 220
12.5 Locus in Analytic Geometry......Page 223
12.6 Areas in Analytic Geometry......Page 225
12.7 Proving Theorems with Analytic Geometry......Page 227
13.1 Inequalities......Page 235
13.2 Indirect Reasoning......Page 240
14.1 Definitions......Page 244
14.2 Deductive Reasoning in Geometry......Page 245
14.3 Converse, Inverse, and Contrapositive of a Statement......Page 246
14.4 Partial Converse and Partial Inverse of a Theorem......Page 248
14.5 Necessary and Sufficient Conditions......Page 249
15.1 Introduction......Page 252
15.2 Duplicating Segments and Angles......Page 253
15.3 Constructing Bisectors and Perpendiculars......Page 254
15.4 Constructing a Triangle......Page 256
15.5 Constructing Parallel Lines......Page 259
15.6 Circle Constructions......Page 260
15.7 Inscribing and Circumscribing Regular Polygons......Page 262
15.8 Constructing Similar Triangles......Page 263
16.1 Introduction......Page 266
16.2 The Proofs......Page 267
17.1 Solids......Page 277
17.2 Extensions to Solid Geometry......Page 281
17.3 Areas of Solids: Square Measure......Page 285
17.4 Volumes of Solids: Cubic Measure......Page 286
18.2 Transformation Notation......Page 292
18.3 Translations......Page 293
18.4 Reflections......Page 295
18.5 Rotations......Page 298
18.6 Rigid Motions......Page 301
18.7 Dihilations......Page 303
19.2 The Postulates of Euclidean Geometry......Page 308
19.3 The Fifth Postulate Problem......Page 309
19.4 Different Geometries......Page 310
Formulas for Reference......Page 313
Answers to Supplementary Problems......Page 317
C......Page 334
M......Page 335
S......Page 336
Z......Page 337