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
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