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Index
A
-
AAS (Angle-Angle-Side) Theorem.
See Angle-Angle-Side (AAS) Theorem
-
AA
∼
tilde operator (Angle-Angle Similarity) Postulate.
See Angle-Angle Similarity (AA
∼
tilde operator ) Postulate
-
absolute value, 20, 28, 832
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activity.
See also Extensions; Technology
- Building Congruent Triangles, 225
- Circle Graphs, 658
- Compass Designs, 42
- Creating Tessellations, 594
- Dynamic. See Dynamic Activity Exploring Spherical Geometry, 179–180
- Exploring the Area of a Circle, 659
- Finding Volume, 725
- The Golden Ratio, 468–469
- Logic and Truth Tables, 96–97
- Measuring From Afar, 515
- Paper Folding and Reflections, 552
- Paper Folding Bisectors, 300
- Paper-Folding Conjectures, 249
- Paper Folding With Circles, 770
- Perpendicular Lines and Planes, 170
- Pythagorean Theorem, 490
- Tracing Paper Transformations, 566–567
- Transforming to Find Area, 614–615
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acute angle, 70
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acute triangle, 494–495
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Addition Property, 113, 323
- addition
- of angles, 30
- of arcs, 650
- of segments, 21
- of vectors, 527
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adjacent angles, 34–35, 73
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adjacent arcs, 611, 649, 650, 676
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algebra.
See also Algebra Review
- exercises, 21, 23, 24, 25, 26, 30, 31, 32, 33, 36, 39, 41, 48, 66, 67, 75, 79, 88, 93, 94, 101, 114, 117, 125, 126, 127, 132, 137, 153, 154, 155, 159, 161, 162, 169, 173, 176, 177, 204, 211, 223, 254, 255, 256, 262, 264, 275, 277, 288–289, 290, 293, 295, 297, 304, 306, 316, 323, 328, 329, 335, 337, 339, 342, 345, 349, 356, 357, 364, 365, 372, 373, 374, 380, 381, 385, 387, 388, 391–392, 395, 397, 398, 405, 410, 419, 425, 434, 436, 438, 439, 442, 445, 446, 457, 458, 459, 463, 465, 467, 475, 476, 477, 481, 482, 483, 487, 492, 495, 496, 497, 502, 504, 505, 514, 520, 537, 620, 628, 640, 656, 673, 698, 706, 716, 723, 731, 759, 767, 769, 775, 777, 787, 788, 791, 793, 794, 795, 815
- reasoning in, 113–116, 129–132
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algebraic expressions, 23, 32, 79
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Algebra Review
- Literal Equations, 698
- Simplifying Radicals, 399
- Solving Inequalities, 323
- Solving Quadratic Equations, 439
- Systems of Linear Equations, 257
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alternate exterior angles, 140, 142–143, 151–152, 206
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Alternate Exterior Angles Theorem, 151–152
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alternate interior angles, 140, 142–143, 206
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Alternate Interior Angles Theorem, 149–152
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altitude
- of cone, 711, 751
- of cylinder, 699, 701, 751
- of parallelogram, 616, 676
- of prism, 699
- of pyramid, 708, 751
- of triangle, 281, 308–312, 341, 343, 460–461
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angle(s)
- acute, 29, 70
- addition of, 30
- adjacent, 34–35, 73
- alternate exterior, 140, 142–143, 151–152, 206
- alternate interior, 140, 142–143, 206
- base, 249, 250, 389
- bisector of, 37, 70, 294–296, 300–304, 341, 342–343, 805
- central, 649, 676, 771–772
- classifying, 29, 72
- complementary, 34–35, 70, 73, 123
- congruence of, 72, 120–123, 132, 220–221, 361–362, 389
- consecutive, 349, 360–361, 420
- constructing, 44
- corresponding, 140, 142–143, 148–152, 206
- of depression, 516–518, 534
- of elevation, 487, 516–518, 534, 536
- exterior, 173–174, 206, 209, 325–326, 352, 355
- formed by a tangent and a chord, 782–783
- inequalities involving angles of triangles, 325–326
- inscribed, 780–783, 811, 813
- lines and, 140–143, 207
- measuring, 27–31, 72, 253, 353–355, 389–390, 392, 419, 420, 629
- obtuse, 29, 70
- opposite, 359–360, 420, 421
- pairs of, 34–35, 70, 73, 140, 142–143
- remote interior, 173–174, 206, 209
- right, 29, 70
- same-side interior, 140, 142–143, 149–152, 206
- straight, 29, 70
- supplementary, 34–35, 70, 73, 122–123, 360–361
- vertex, 250, 273
- vertical, 34–35, 70, 73, 120–123
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Angle Addition Postulate, 30
-
Angle-Angle-Side (AAS) Theorem, 236–237, 274
-
Angle-Angle Similarity (AA
∼
tilde operator )
-
Postulate, 450–451
-
angle bisector, 37, 70, 294–296, 300–304, 341, 342–343, 805
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Angle Bisector Theorem, 295, 342
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angle of rotation, 559
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Angle-Side-Angle (ASA) Postulate, 234, 235–236, 274
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Angle-Sum Theorems, 353–355, 421
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apothem, 629–631, 643–645, 676, 678
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applications
- accessibility, 195
- advertising, 94
- aerial views, 9, 144, 520
- agriculture, 637, 663
- alphabets, 571
- archaeology, 412, 466, 775
- archery, 670
- architecture, 9, 10, 143, 254, 289, 445, 446, 465, 504, 511, 647, 714, 727, 728, 729, 731
- art, 437, 442, 445, 469, 563, 595, 632
- astronomy, 497, 513, 672, 739, 768
- automobiles, 467
- aviation, 436, 503, 520, 530, 531, 755