Holt McDougal Fuse Geometry 2012 correlated to Texas Essential Knowledge and Skills Geometry
Holt McDougal Fuse Geometry 2012 correlated to the Texas Essential Knowledge and Skills for Mathematics High School Geometry 111.34. Geometry (b) Knowledge and skills. (1) Geometric structure. The student understands the structure of, and relationships within, an axiomatic system. The student is expected to: develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems; SE: 6 11, 20 27, 43 49, 155 161, 162 169, 172 178, 231 238, 250 257, 260 267, 274 277, 312 318, 319 325, 326 332, 334 339, 344 351, 352 357, 360 367, 368 374, 394 400, 403 409, 410 417, 420 427, 430 437, 439 447, 482 491, 495 501, 502 508, 509 516, 534 539, 626 631, 677 685, 792 800, 802 809, 820 827, 830 837, 840 846 recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes; and compare and contrast the structures and implications of Euclidean and non-euclidean geometries. SE: 50 55, 78, 146 151, 231 238, 268, 330, 416, 446, 547, 584, 608, 683, 755, 772, 814, 852 SE: 34 (2) Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures. The student is expected to: use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships; and SE: 294 295, 319 325, 326 332, 392 393, 402, 420 427, 439 447, 495 501, 509 516, 604 610, 611 617, 619 625, 650 657, 687 688, 792 800, 820 827 make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. SE: 74 79, 88 93, 162 169, 172 178, 260 267, 285 291, 312 318, 333, 438
(3) Geometric structure. The student applies logical reasoning to justify and prove mathematical statements. The student is expected to: determine the validity of a conditional statement, its converse, inverse, and contrapositive; SE: 81 87 construct and justify statements about geometric figures and their properties; use logical reasoning to prove statements are true and find counter examples to disprove statements that are false; SE: 96 101, 239 245, 250 257, 268 273, 274 277, 285 291, 420 427, 430 437, 466 471, 482 491 SE: 94 95, 162 169 use inductive reasoning to formulate a conjecture; and SE: 74 79 (E) use deductive reasoning to prove a statement. SE: 88 93, 110 116, 117, 118 125, 126 127, 420 427, 472 479 (4) Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. Representative Pages: SE: 12, 13 19, 20 27, 36 41, 50 55, 146 151, 155 161, 172 178, 188 189, 198 199, 216 223, 224 229, 239 245, 260 267, 285 291, 312 318, 319 325, 326 332, 352 357, 368 374, 394 400, 430 437, 472 479, 562 567, 604 610, 619 625, 677 685, 802 809 (5) Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to: use numeric and geometric patterns to develop algebraic expressions representing geometric properties; SE: 74 79 use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles; use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations; and identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples. SE: 231 238, 394 400, 403 409 SE: 626 631, 643 649 SE: 231 238, 360 367, 368 374 2
(6) Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems. The student is expected to: describe and draw the intersection of a given plane with various three-dimensional geometric figures; use nets to represent and construct three-dimensional geometric figures; and use orthographic and isometric views of threedimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems. (7) Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly. The student is expected to: use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures; SE: 43 49, 50 55, 182 187, 190 197, 198 199, 216 223, 274 277, 279 284, 326 332, 334 339, 410 417, 430 437, 472 479, 509 516, 604 610, 611 617, 619 625, 847 853 use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons; and derive and use formulas involving length, slope, and midpoint. SE: 146 151, 152 153, 155 161, 162 169, 170 171, 172 178, 182 187, 188 189, 190 197, 198 199 SE: 43 49, 182 187 (8) Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations. The student is expected to: find areas of regular polygons, circles, and composite figures; SE: 36 41, 677 685, 688 693, 694 700, 701 find areas of sectors and arc lengths of circles using proportional reasoning; SE: 810 815 derive, extend, and use the Pythagorean Theorem; SE: 43 49, 359, 360 367 find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations; SE: 749 756, 757 764, 766 773 TE: 749 756, 757 764, 766 773 3
(E) use area models to connect geometry to probability and statistics; and SE: 716 717, 718 724 (F) use conversions between measurement systems to solve problems in real-world situations. SE: 677 685, 688 693 (9) Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures. The student is expected to: formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models; SE: 155 161, 162 169, 172 178 formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models; formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models; and analyze the characteristics of polyhedra and other threedimensional figures and their component parts based on explorations and concrete models. SE: 246, 248 249, 250 257, 258 259, 260 267, 268 273 SE: 792 800 (10) Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems. The student is expected to: use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane; and SE: 216 223 justify and apply triangle congruence relationships. SE: 224 229, 248 249, 250 257, 260 267, 268 273 4
(11) Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. The student is expected to: use and extend similarity properties and transformations to explore and justify conjectures about geometric figures; SE: 472 479, 509 516, 534 539, 650 657 use ratios to solve problems involving similar figures; SE: 466 471, 502 508 develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods; and describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems. SE: 360 367, 466 471, 480 481, 482 491, 495 501 SE: 710 715 5