Index

30-60-90 triangle, 190, 233

36-72-72 triangle, 226

360 theorem, 96, 97

45-45-90 triangle, 190, 233

60-60-60 triangle, 189

AA congruence theorem for asymptotic

triangles, 353

AA similarity theorem, 216

AAA congruence theorem in hyperbolic

geometry, 338

AAA construction theorem, 191

AAASA congruence, 197, 354

AAS congruence theorem, 119

AASAS congruence, 179

ABCD property of rigid motions, 441

absolute value, 434

acute angle, 88

acute triangle, 105

adapted coordinate function, 72

adjacency lemma, 98

adjacent angles, 90, 91

adjacent edges of a polygon, 156

adjacent interior angle, 113

admissible decomposition, 201

algebraic number, 317

all-or-nothing theorem, 333

alternate interior angles, 150

alternate interior angles postulate, 323

alternate interior angles theorem, 150

converse, 185, 323

altitude concurrence theorem, 269

altitude of a triangle, 144, 208

intersects interior of a side, 144

to the base of an isosceles triangle, 145

to the hypotenuse, 144

to the longest side, 144

Amtrak model, 29

and (logical conjunction), 385

angle, 83

acute, 88

included between two sides, 104

inscribed in a semicircle, 257

inscribed in an arc, 257

obtuse, 88

of a polygon, 156

of a triangle, 103

of an asymptotic triangle, 351

on a side of a line, 149

opposite a side, 104

proper, 84

right, 88

straight, 84

zero, 84

angle addition theorem, 90

angle bisector, 100, 147

angle bisector concurrence theorem, 268

angle bisector proportion theorem, 219

angle bisector theorem, 147

converse, 149

angle construction theorem, 88

angle criterion for convexity, 160

angle measure, 54, 85

between two lines, 357

in taxicab geometry, 138

in the Cartesian plane, 125

455