Index

A of square 83 of trapezoid 89 Addition of vectors 296 of triangle 86 Additive inverse 297 Area under dilation 220, 272 Adjacent angles 18 Area under shearing 267 d'Alembert 117 ASA 181, 381 Alternate angles 49 Associativity 297 Altitude 86 Axioms 3, 31 Angle bisector 18, 25, 196 Axis 65 Angle of incidence 63 Angle of polygon 166 Angle of reflection 62 B Angles 13 adjacent 18 Ball 281 alternate 49 Band 223, 231 central 148 Base angles 140 inscribed 170 Base of cylinder 263 opposite 28, 30, 58 Base of trapezoid 89 parallel 49 Base of triangle 86 polygon 166, 168 Bisector 18, 107, 124 right 16 Blow up 212 straight 15 Boxes 261 vertical 28 Angles of triangle 50 c Apollonius theorem 154 Arc 14, 148 Cancellation law 308 Area 81 Central angle 148 of circle 221 Chord 132 of parallelogram 193 Circle 10, 119, 128, 148, 158, 235, 290 of rectangle 83 Circumference 11, 235, 290 of right triangle 84 Circumscribed 128 of sector 224-230 Collinear 4 of sphere 292 Commutativity 296 392 INDEX

Component 311, 317 F Composition of isometries 369-372 Concentric circles 158 Feynman 188, 351 Conclusion 13 Fixed point 385 Cone 274, 275 Forty-five degree triangle 200 Congruence 178, 377 Frustrum 281 Congruent triangles 178, 381 Full angle 16 Construction of triangle 6 Contradiction 38 Converse 13 G Convex polygon 165 Coordinate 67, 115, 117 Graph 73 Corollary 141 Cylinder 263 H Half line 2 D Height 86, 89, 263, 274, 275 Hexagon 163 d'Alembert 117 Higher dimensional space 114 Degree 16 Hypotenuse 46 Diagonal 48, 167, 196 Hypothesis 13 Diameter of circle 154, 235, 240 Diderot 117 Dilation 113, 211 of area 220 I of length 232 Identity mapping 343, 373 of rectangle 218 If and only if 8, 12 of triangles 248 Image 324, 328, 331 of volume 271, 273 Incidence 63 Dimension 117 Inscribed angle 149, 170 Disc 10 Inscribed circle 197 DIST 8 Inscribed polygon 170, 172 Distance 2, 8, 72, 100, 112, 265 Intercept arc 148 Distance from point to line 38 Inverse 297, 373 Distance preserving 357 ISOM 359 Distance under dilation 232 Isometry 357, 388 Dot product 301, 316 Isosceles triangle 4, 136, 142 d(P, Q) 2, 8 Isosceles triangle theorem 139, 189

E L Ellipse 186 Laser beams 62, 64 Encyclopedia 117 Latitude 20 Equal areas 187 Legs of right triangle 44 Equality 5, 342 Lemma 125 Equation of circle 119, 148 Length under dilation 232 of line 75, 312 LIN 1 of plane 319 Line segment 1 Equidistant 112, 123, 125 Line symmetry 326, 329 Equilateral triangle 4, 140 Lines 1 Euclid's tests for congruence 180-183, equation of lines 75, 312 381 Located vector 296 INDEX 393

M Q Mapping 331 Quadrant 68 Midpoint 124 Quadrilateral 39, 163 Mirror image 324

R Ray 2 0 Rectangle 39 Obtuse angle 56 Reflection 62, 328, 332, 337 Opposite angles 28, 30 Regular polygon 169 of a parallelogram 58 Rhombus 130 Opposite sides of parallelogram 192 Right angle 16 Ordinary equation for line 312 Right circular cone 274 Origin 65, 68 Right cylinder 263 Right prism 263 Right triangle 44, 47, 95, 110, 142, 200 p Rotation 341 RT 47 PAR 3 Parallel 2, 39, 49, 64 Parallel angles 49 s Parallel distance 39 Parallelepiped 268 Same 5 Parallelogram 39, 58, 192 SAS 183, 381 Parallelogram law 298 Scalar product 301, 316 PD 39 Sectors 224, 229 Pentagon 163 SEG 9 Perimeter 169 Segment 1, 9 PERP 37 Shearing 266, 269 Perpendicular 36, 43, 305-306, 312, Similar triangles 245, 248 317, 319, 354 Slope 76, 315 Perpendicular bisector 107, 124, 132 SP 1 through SP 4 301, 302 of sides of triangle 128 Special pyramid 276, 279 Perpendicular construction 43 Special triangle 200 Perpendicular distance 38, 365 Sphere 122, 281 Perpendicular height 365 Square 40 lines 314 sss 180, 381 planes 319 Straight angle 15 Plane 319 Sum of angles of triangle 50 Polygon 164, 168 Sum of vectors 296 regular, 169 Supplementary angles 17 Postulate 3, 31 Symmetry 324 Preserve distance 357 Product of point by number 212 T Projection 115, 311, 318, 354 Proof 29 Tangent to circle 155 by contradiction 38 Theorem 30 Protractor 21 Thirty-sixty triangle 201 Prism 363 Torus 243 Pyramid 275-281 Transformation 321 Pythagoras theorem 95, 110, 142 Translation 347 Pythagorean triple 104 Trapezoid 89 394 INDEX

Triangle 4, 6 Vertex 2, 163, 274 equilateral 4 Vertical angle 28 isosceles 4 Volume right 44, 47, 95, 110, 142, 200 of ball 281 similar 245, 248 of box 261 Triangle inequality 8 of cone 274, 276 Triangular region 4 of cylinder 263, 265, 281 of pyramid 278 u Volume under dilation 271, 273 Volume under shearing 268 Unit point 311 v z Value 332 Vector 296, 346 Zero element 297