CORRELATION TO GEORGIA (GRADES 9-12) SUBJECT AREA: Mathematics COURSE: 27. 06300 TEXTBOOK TITLE: PUBLISHER: Geometry: Tools for a Changing World 2001 Prentice Hall 1 Solves problems and practical applications using appropriate approaches and tools (including calculators and computers) and judges the reasonableness of results. Problem Solving, Visualizing, Reasoning SE: 4-10, 46-52, 207-211 CP: 88, 206, 284, 322, 343 MR: 199, 306, 369, 555 OY: 7-9, 50-52, 156, 209-211, 260, 357, 482, 554, 571, 597 RW: 5, 207, 280, 288, 326, 344, 363, 545 SH: 660-665 TD: 5, 46, 48 WT: 4, 47, 209 Chapter Project: 3, 10, 22, 31, 44, 58, 67, 74, 81, 95, 107, 115, 116, 123, 137, 143, 150, 158, 171, 173, 181, 187, 198, 205, 225, 233, 241, 248, 254, 273, 290, 292, 301, 306, 314, 329, 335, 353, 361, 369, 382, 391, 396, 398, 405, 412, 424, 438, 440, 447, 453, 468, 476, 488, 495, 502, 516, 523, 529, 536, 543, 549, 560, 567, 577, 578, 585, 591, 605, 618, 627 Geometry at Work: 38,115, 172, 336, 419, 577, 626 Critical Thinking: 13, 21, 25, 37, 51,61, 72, 81, 87, 98, 103, 104, 106, 127, 128,130, 139, 145, 146, 153, 160, 167, 170, 191, 193, 202, 209, 229, 230, 245, 269, 277, 281, 308, 320, 329, 335, 343, 348, 349, 350, 352, 357, 368, 373, 378, 380, 381, 382, 388, 396, 400, 410, 412, 416, 422, 426, 474, 484, 487, 498, 508, 515, 521, 532, 534, 546, 554, 560, 566, 580, 590, 598, 605, 611, 612, 617, 618, 623 1
2 Uses algebraic skills and concepts to solve geometric problems throughout geometry. Problem Solving, Visualizing, Reasoning 3 Uses visualization skills to explore and interpret both two-and three-dimensional geometric figures using such topics as projections, cross sections, and locus problems. Problem Solving, Visualizing, Reasoning 4 Uses inductive and deductive reasoning to reach conclusions, identifies conjectures and counterexamples, and describes the nature of a deductive mathematical system. Problem Solving, Visualizing, Reasoning SE: 83-87, 102-104, 256-262, 496-500, 517-521, 586-591 CP: 88, 268, 482 MR: 88, 268, 591 MT: 11, 23, 82, 89, 131, 212, 255, 307, 370, 439, 477, 503, 562, 592 OY: 86, 87, 259-262, 266-268, 452, 466, 474, 499-501, 514, 588-590 RW: 54, 102, 134, 257, 266, 497, 587 SH: 673-680 TD: 25, 46, 47, 496, 586 WT: 499, 586 SE: 109-115, 302-306, 384-391 MR: 172, 211, 577 MT: 384 OY: 36, 57, 87, 112-114, 156, 216, 268, 271, 304, 305, 313, 327, 329, 375, 388-391, 417, 423, 481, 522, 576, 604 RW: 303, 349, 387 TD: 109, 302, 385 WT: 112, 302, 303, 388 SE: 4-10, 46-52 MT: 75, 200, 315, 362 OY: 7-9, 21, 50-52 RW: 5 TD: 5, 46, 48 WT: 4, 47, 68, 77, 84, 125, 201, 420 WU: 59, 60 Chapter Project: 187, 198, 205, 225, 233, 516 2
5 Recognizes valid deductive reasoning, constructs and uses if-then, converse, inverse, and contrapositive statements. Problem Solving, Visualizing, Reasoning 6 Uses formal and/or informal logic reasoning processes. Problem Solving, Visualizing, Reasoning SE: 46-52, 182-187 MR: 549 OY: 50-52, 185-187 TD: 46, 48, 182 WT: 47 WU: 60, 234 Chapter Project: 205 SE: 4-10, 46-52, 182-187, 194-199, 207-211 MR: 22 OY: 7-10, 16, 50-52, 71, 73, 87, 185-187, 191, 196-198, 198, 209-211, 218, 223, 261, 452, 467, 522, 612 RW: 5, 207 SH: 660-665 TD: 5, 46, 48, 182, 194, 207 WT: 4, 47, 196, 209 WU: 59, 60, 234 Chapter Project: 3, 10, 22, 31, 44, 58, 67, 74, 81, 95, 107, 115, 116, 123, 137, 143, 150, 158, 171, 173, 181, 187, 198, 205, 225, 233, 241, 248, 254, 273, 290, 292, 301, 306, 314, 329, 335, 353, 361, 369, 382, 391, 396, 398, 405, 412, 424, 438, 440, 447, 453, 468, 476, 488, 495, 502, 516, 523, 529, 536, 543, 549, 560, 567, 577, 578, 585, 591, 605, 618, 627 3
7 Identifies, describes, and contrasts points, lines, planes, segments, and rays. Points, Lines, and Planes 8 Identifies, defines, estimates, and measures segments and angles (acute, obtuse, right, straight, complementary, supplementary, adjacent, vertical, congruent, and linear pair). Points, Lines, and Planes 9 Identifies and defines or describes properties associated with points (distance, between, collinear, coplanar), segments (midpoint, congruence, bisector), angles (bisector, congruence, interior, exterior), and lines and planes (perpendicular, parallel, intersecting). Points, Lines, and Planes SE: 12-22 CP: 31 MR: 17, 22, 31, 44, 510 OY: 15-17, 20-22 TD: 12, 18 WT: 12, 20 WU: 60 SE: 24-44, 46-52 CP: 31 MR: 31, 38, 81, 232, 453, 591 MT: 45 OY: 28-31, 36, 37, 43, 44, 50-52 RW: 33 TD: 25, 32, 39, 48 WT: 24, 32, 39, 47 WU: 60, 61 SE: 12-57, 68-74, 83-88, 219-232, 363-383 CP: 31, 383 MR: 17, 22, 31, 38, 44, 52, 225, 232, 453 MT: 45, 75, 362 OY: 15-17, 20-22, 28-30, 35-37, 43, 44, 50-52, 56, 57, 71-73, 223-225, 230-232, 366-368, 373-376, 380-382 RW: 32, 54, 70, 220, 222, 228, 363, 365, 373 TD: 12, 18, 25, 32, 39, 54, 219, 363, 364, 371, 377 WT: 12, 20, 24, 32, 39, 53, 219, 221, 364, 371 WU: 60-62, 118, 399, 400 4
10 Classifies triangles as acute, right, obtuse, equilateral, isosceles, scalene; and classifies polygons as regular, convex, congruent. Points, Lines, and Planes 11 Recognizes parallel lines and planes, skew lines, and pairs of angles formed when two lines are cut by a transversal (alternate and same side, interior and exterior, corresponding). Points, Lines, and Planes 12 Applies basic facts about points, lines and planes, and about perpendicular and parallel lines and planes. Points, Lines, and Planes SE: 68-81, 102-107, 188-193 CP: 88, 108 MR: 49, 468 MT: 75 OY: 71-74, 79-81, 105-107, 191-193 RW: 70, 79, 102, 190 TD: 68, 76, 77, 102, 188 WT: 68, 77, 104, 188 WU: 118, 235 SE: 18-22, 362-383 CP: 383 MT: 362 OY: 20-22, 366-369, 373-376, 380-382 RW: 363, 365, 373 TD: 18, 363, 364, 371, 377 WT: 20, 364, 371 WU: 399, 400 SE: 12-22, 32-38, 83-88, 363-383 CP: 383 MR: 17, 502 MT: 45, 362 OY: 15-17, 20-22, 35-37, 86-88, 366-368, 380-382 RW: 33, 363, 365 TD: 12, 18, 32, 85, 363, 364, 377 WT: 12, 18, 32, 84, 364 WU: 60, 61, 399, 400 5
13 States and applies the triangle sum, exterior angles, and polygon angle sum theorems. Points, Lines, and Planes 14 Identifies congruent figures and recognizes congruence in practical applications. Congruence 15 Uses tools such as compass and straightedge, paper folding, tracing paper, ruler, or computer to construct congruent segments, angles, triangles, and circles, an angle bisector; a perpendicular bisector; a perpendicular line from a point on a line; parallel lines; proportional segments; tangents; and inscribed and circumscribed polygons. SE: 68-81, 194-198 MR: 81 MT: 75 OY: 71-73, 79-81 RW: 70, 79 TD: 68, 71 WU: 117 SE: 39-44, 102-107 MT: 45 OY: 43, 44, 105-107 RW: 102 TD: 25, 39, 102 WT: 39, 104 SE: 39-44, 377-383, MR: 108, 225, 376, 412, 419, 424, 431, 432, 549, 577, 597, 604, 612, 613 MT: 45, 362 OY: 43, 170 SH: 666 TD: 39 WT: 39 Congruence 6
16 Identifies congruent triangles and right triangles using basic congruence postulates and theorems. Congruence 17 Uses properties of congruence to establish properties or test conjectures involving one and two triangle inequality relationships; isosceles and equilateral triangles; medians, altitudes, and bisectors of triangles and special quadrilaterals. Congruence SE: 406-440 CP: 425 MR: 193 MT: 413 OY: 409-412, 416-418 422-424, 429-431, 436-438 RW: 407, 415, 421, 427 TD: 406, 408, 414, 420, 426, 433 WT: 406, 408, 414, 420, 433, 435 WU: 441-443 Chapter Project: 412, 424, 438, 440 SE: 68-73, 188-193, 213-232, 426-438, 448-476 CP: 225, 460 MR: 225, 432, 438,453, 460, 468, 476 MT: 226, 461, 469 OY: 71-73, 191-193, 216-218, 223, 224, 230-232, 429-432, 436-438, 451-453, 457-459, 465-468, 473-476 RW: 190, 215, 220, 222, 228, 427, 450, 457, 471 TD: 188, 214, 215, 219, 222, 227, 426, 433, 448, 455, 463, 470 WT: 188, 213, 214, 219, 221, 227, 433, 435, 448, 454, 462, 470 WU: 235-237, 441-443, 489 491 7
18 States and applies properties of triangles and quadrilaterals such as parallelograms, rectangles, rhombi, squares, and trapezoids. Congruence 19 Uses properties of quadrilaterals to establish and test relationships involving diagonals, angles, and lines of symmetry. Similarity SE: 90-95, 188-218, 448-487 CP: 206, 460, 482 MR: 193, 199, 206460, 476, 482 MT: 200, 212, 461, 469 OY: 93-95, 191-193, 196-198, 203-205, 209-211, 216-218, 451-453, 457-459, 465-468, 473-476, 480, 481, 485-487 RW: 190, 203, 207, 215, 450, 457, 465, 471, 479, 484 TD: 90, 188, 194, 201, 214, 215, 448, 455, 463, 470, 478, 483 WT: 90, 188, 196, 201, 207, 209, 213, 448, 454, 462, 470, 478, 483 WU: 234-237, 489-491 Chapter Project: 447, 453, 468, 476, 488 SE: 454-459, 462-467, 478-487 CP: 460 MR: 502 MT: 461 OY: 457-459, 465-467, 480, 481, 485-487 RW: 457, 465, 479, 484 TD: 455, 463, 478 WT: 462, 478 WU: 489 491 8
20 Identifies similar figures in practical applications; identifies similar triangles and other similar polygons by using their properties. Similarity 21 Recognizes and applies properties of similar polygons using ratio and proportion. Similarity 22 Applies properties dealing with parallel lines and proportion. Similarity SE: 496-523 CP: 510, 529 MR: 510 OY: 499-502, 507-509, 514-516, 520-522 RW: 497, 505, 513, 518 SH: 675 TD: 496, 504, 511, 517, 519 WT: 499, 504, 511, 517, 519 WU: 537-539 Chapter Project: 495, 502, 516, 523, 529, 536 SE: 496-502, 511-525 CP: 510, 529 MR: 510, 619 MT: 503 OY: 499-501, 514-516, 520-522 RW: 497, 513, 518 SH: 675 TD: 496, 511, 517, 519 WT: 499, 511, 517, 519 WU: 537-539 SE: 517-523 CP: 529 OY: 520-523 RW: 518 TD: 483, 517, 519 WT: 517, 519 9
23 Solves problems involving similar polygons. Similarity 24 States and applies the Pythagorean Theorem and its converse. Right Triangles 25 States and applies properties of special right triangles, such as 45-45-90 and 30-60-90 triangles. Right Triangles SE: 102-107, 524-535 MR: 619 MT: 530 OY: 105-107, 527, 528, 533-535 RW: 102, 526, 533 TD: 102, 525, 531 WT: 104, 524, 531 SE: 256-268 CP: 268 MR: 599 MT: 255 OY: 259-262, 266-268 RW: 257, 264, 266 TD: 256, 263, 264 WT: 256, 263, 264 WU: 294 SE: 263-268 CP: 268 OY: 266-268 RW: 264 TD: 263, 265 WT: 263, 264 10
26 Identifies and evaluates tangent, sine, and cosine ratios for an acute angle of a right triangle, uses a table, calculator or computer to find the ratio for a given angle or find the angle for a given ratio. Right Triangles 27 Use the tangent, sine, and cosine ratios for right triangles to solve application patterns such as indirectmeasurement problems. Right Triangles SE: 544-555 CP: 561 MR: 599, 626 MT: 550 OY: 546-548, 554, 555 RW: 545, 552 TD: 544, 551 WT: 544, 553 WU: 579-581 Chapter Project: 543, 549, 560, 567, 577, 578 SE: 544-561, 573-577 CP: 561 MR: 599, 626 MT: 550 OY: 546-548, 554, 555, 558-560, 575-577 RW: 545, 552, 557, 558, 574 TD: 544, 551, 556, 573 WT: 544, 553 WU: 579-581 Chapter Project: 543, 549, 560, 567, 577, 578 11
28 Identifies and defines circles and their parts (center, arc, interior, exterior); segments and lines associated with circles (chord, diameter, radius, tangent, secant); properties of circles (congruent, concentric, tangent); relationship of polygons and circles (inscribed, circumscribed); angles (central; inscribed; formed by tangents, chords and secants). Circles 29 Applies geometric relationships to solving problems, such as relationships between lines and segments associated with circles, the angles they form, and the arcs they extend; and the measures of these arcs, angles and segments. Circles SE: 96-101, 586-626 CP: 606, 619 MR: 606, 613 MT: 592, 620 OY: 99-101, 588-591, 596-599, 603-605, 610-613, 617, 618, 623-625 RW: 97, 587, 594, 602, 616, 623 TD: 96, 586, 593, 596, 600, 607, 614, 621 WT: 96, 586, 593, 595, 600, 607, 614, 621 WU: 628-630 Chapter Project: 585, 591, 605, 618, 627 SE: 96-101, 586-626 CP: 606, 619 MR: 606, 613 MT: 592, 620 OY: 99-101, 588-591, 596-599, 603-605, 610-613, 617, 618, 623-625 RW: 97, 587, 594, 602, 616, 623 TD: 96, 586, 593, 596, 600, 607, 614, 621 WT: 96, 586, 593, 595, 600, 607, 614, 621 WU: 628-630 Chapter Project: 585, 591, 605, 618, 627 12
30 Defines and differentiates among perimeter, area, and volume, and the appropriate unit for each. Perimeter, Area, and Volume 31 Finds the perimeter of polygons, the circumference of circles, and arc lengths. Perimeter, Area, and Volume SE: 242-254, 323-326, 330-347 CP: 268, 284, 322, 343 MR: 306, 314, 336, 343 MT: 291 OY: 245-248, 251-254, 327-329, 333-335, 340-342, 346, 347 RW: 244, 251, 326, 331, 338, 345 SH: 673, 680 TD: 242, 249, 251, 323, 331, 337, 344 WT: 242, 249, 251, 323, 330, 337, 344 WU: 293-295, 354-356 Chapter Project: 241, 248, 254, 273, 290, 293 SE: 242-248, 279-284 CP: 268, 284, 322 MR: 306, 314, 336, 352 MT: 291 OY: 245-248, 282-284 RW: 244, 280 SH: 673, 680 TD: 242, 279 WT: 242, 279 WU: 293 296 13
32 Finds the areas of triangles, parallelograms, rectangles, squares, trapezoids, regular polygons, circles, and sectors. Perimeter, Area, and Volume SE: 242-254, 269-291 CP: 268, 284, 322 MR: 306, 314, 336, 535 MT: 291 OY: 245-248, 252-254, 271-273, 276-278, 282, 283, 288-290 RW: 244, 251, 270, 275, 280, 286 SH: 680 TD: 242, 249, 251, 269, 274, 279, 285 WT: 242, 249, 251, 269, 279, 285 WU: 293-296 Chapter Project: 241, 248, 254, 273, 290, 293\ M9.12.33 Identifies polyhedrons, including prisms, pyramids, cubes and tetrahedrons; cylinders, cones, spheres; faces; edges; vertices; bases; and lateral edges. Perimeter, Areas, and Volume SE: 302-322 MT: 315 OY: 304-306, 312-314, 319-321 RW: 303, 311, 317 SH: 680 TD: 303, 302, 309, 316 WT: 302, 303, 308, 319 WU: 354-356 14
34 Finds the lateral and total areas of right prisms, regular pyramids, right circular cylinders, and cones; and finds the surface area of spheres. Perimeter, Areas, and Volume 35 Find the volume of solids composed of prisms, pyramids, cylinders, cones or spheres. Perimeter, Areas, and Volume SE: 308-322, 337-347 CP: 322, 343 MR: 529 MT: 315 OY: 312-314, 319-321, 340-342, 346, 347 RW: 311, 317, 338, 345 SH: 680 TD: 309, 316, 337, 344 WT: 308, 319, 337, 344 WU: 354-357 SE: 323-347 CP: 343 MR: 343, 529 OY: 327-329, 333-335, 340-342, 346, 347 RW: 326, 338, 345 SH: 680 TD: 324, 331, 337, 344 WT: 323, 330, 337, 344 WU: 354-356 15
36 Compares the areas of similar polygons and the volumes of similar solids. Perimeter, Areas, and Volume 37 Solves problems involving perimeter, area, and volume. Perimeter, Areas, and Volume SE: 524-535 CP: 529 MT: 530 OY: 527-529, 533-535 RW: 526 TD: 525, 531 WT: 524, 531 WU: 539 SE: 242-254, 269-278, 285-290, 308-343, 524-535 CP: 268, 284, 322, 529 MR: 306, 314, 336, 352, 535, 529 MT: 291, 315, 530 OY: 245-248, 252-254, 270-273, 276-278, 286-290, 312-314, 319-321, 327-329, 333-335, 340-342, 527-529, 533-535 RW: 251, 270, 274, 286, 311, 317, 326, 338, 526 TD: 242, 249, 251, 269, 274, 285, 309, 316, 324, 331, 337 WT: 242, 249, 251, 269, 285, 308, 319, 323, 330, 337, 524 WU: 293-296, 539 Chapter Project: 241, 248, 254, 273, 290, 292, 301, 306, 314, 329, 335, 353 16
38 Finds the images of geometric figures under distancepreserving transformations such as line reflections, translations and rotations. Transformational Geometry 39 Finds the image of figures under dilations. Transformational Geometry 40 Examines and applies basic properties of line reflections, translations, rotations, dilations and their compositions. Transformational Geometry SE: 124-143, 152-158 CP: 143, 158 MR: 130, 143, 150 OY: 127-129, 135-137, 141-143, 155-158 RW: 127, 134, 140, 153 TD: 124, 126, 132, 138, 152 WT: 124, 132, 138, 154 WU: 174-176 Chapter Project: 123, 137, 143, 150, 158, 171, 173 SE: 166-171 OY: 168-171 TD: 166 WT: 166 WU: 177 SE: 124-158, 166-171 CP: 143, 158 MR: 130, 143, 150 MT: 151 OY: 127-129, 135-137, 141-143, 147-149, 155-158, 168-171 RW: 127, 134, 140, 145, 153 TD: 124, 126, 132, 138, 144, 152, 166 WT: 124, 132, 138, 144, 154, 166 WU: 174-176 Chapter Project: 123. 137, 143, 150, 158, 171, 173 17
41 Use transformations to examine symmetry, similarity, and congruence of geometric figures. Transformational Geometry 42 Identifies and graphs ordered pairs of numbers in the coordinate plane. Coordinate Geometry 43 Applies the distance and midpoint formulas. Coordinate Geometry SE: 124-137,152-171 CP: 143, 158 MR: 143 OY: 127-130, 135-137, 142, 155-157, 168-171 RW: 127, 134, 153, 167 TD: 124, 126, 132, 152, 166 WT: 125, 132, 154 WU: 174 177 SE: 53-57 CP: 88 MR: 47 OY: 56, 57 RW: 54 TD: 54 WT: 53 WU: 62 SE: 32-38, 53-57, 96, 97, 201-204, 243, 483-487 MR: 108, 199, 206, 225, 248, 369 OY: 35-37, 56, 57, 94, 99, 204, 261, 485-487 RW: 33, 54, 484 TD: 32, 54 WT: 32, 53 WU: 61, 62 18
44 Finds the slope of a line, writes an equations of a line, and graphs equations of lines. Coordinate Geometry 45 Finds the coordinates of the point of intersection of two lines, using algebra, graphing, and appropriate technology. Coordinate Geometry 46 Uses coordinate methods to explore, make conjectures or prove properties of geometric figures, using tools such as algebra, graphing, and appropriate technology. Coordinate Geometry SE: 82-89 MR: 187 MT: 23, 82, 89, 370 OY: 86-88, 231 SH: 670, 677-679, 681 TD: 83, 85 WT: 84 WU: 118 SE: 83-88, 450 MT: 89, 370 OY: 86, 87, 452, 466, 486, 487 SH: 681 SE: 201-205, 478-487 MR: 108, 143, 187, 199, 206, 225, 248, 369 OY: 94, 99, 128, 136, 157, 170, 186, 191, 203-205, 231, 480, 481,485-487 RW: 479, 484 TD: 201, 478, 483 WT: 478, 483 WU: 174, 491 19