Publisher: Pearson Ed. Inc., publishing as Prentice Hall Program Title: Prentice Hall Geometry 2011 Components: SE, TE Grade Level(s): 9-12 Intended Audience: s Map - Basic Comprehensive Program Grades Eight Through Twelve - Mathematics The standards for grades eight through twelve are organized differently from those for kindergarten through grade seven. In this section strands are not used for organizational purposes as they are in the elementary grades because the mathematics studied in grades eight through twelve falls naturally under discipline headings: algebra, geometry, and so forth. Many schools teach this material in traditional courses; others teach it in an integrated fashion. To allow local educational agencies and teachers flexibility in teaching the material, the standards for grades eight through twelve do not mandate that a particular discipline be initiated and completed in a single grade. The core content of these subjects must be covered; students are expected to achieve the standards however these subjects are sequenced. FOR LEA USE ONLY # Citation Citation Evaluator Notes DISCIPLINE Geometry The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems. math812grsm.doc 1
8-12 1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. 8-12 2.0 Students write geometric proofs, including proofs by contradiction. 8-12 3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. 11-19, 71, 82-88, 106-112, 113-119, 120-127, 130-132 115-118, 120-126, 132, 150, 153, 155, 158-162, 166-168, 208, 221-224, 226-233, 234-241, 244-248, 258-264, 266-271, 274-276, 317-322, 335-338, 344, 361, 364-366, 370-374, 384, 386-388, 414-418, 422-424, 450-458, 481 84-86, 90-95, 96-97, 98-104, 106-112, 113-119, 130-132 math812grsm.doc 2
8-12 4.0 Students prove basic theorems involving congruence and similarity. 8-12 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. 8-12 6.0 Students know and are able to use the triangle inequality theorem. 8-12 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 122-126, 132, 221-224, 226-233, 234-241, 244-248, 258-264, 274-276, 450-453, 455-458, 481 221-224, 226-233, 234-241, 244-248, 258-264, 265-271, 274-276, 450-458, 481 327-331, 344 148-155, 156-163, 165-168, 207-208, 359-366, 367-374, 375-382, 383-388, 389-397, 401-405, 421-424, 651-657, 660-666, 679-680, 760-769, math812grsm.doc 3
771-779, 780-787, 790-797, 812-814 8-12 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 8-12 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. 8-12 10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. 59-67, 68, 74, 614-615, 616-622, 623-628, 629-634, 643-648, 651-657, 659, 660-666, 667, 669-674, 677-680, 700-707, 708-715, 717-724, 725, 726-732, 733-740, 752-754 700-706, 708-715, 717-724, 726-732, 733-739, 752-754 59-67, 74, 614-615, 616-622, 623-628, 629-634, 643-648, 677-679 math812grsm.doc 4
8-12 11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. 8-12 12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. 8-12 13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. 8-12 14.0 Students prove the Pythagorean theorem. 8-12 15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. 8-12 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 635-641, 678, 741, 742-749, 754 171-178, 209, 250-256, 275, 319-322, 325-331, 333-339, 344, 352, 353-358, 367-374, 375-382, 389-397, 400-405, 421-424, 491-498, 499-505, 535, 825 171-178, 209, 325-326, 328, 344, 360-361, 365 491-498, 535 43-48, 73, 182-188, 209 490, 491, 497 math812grsm.doc 5
8-12 17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 8-12 18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x)) 2 + (cos(x)) 2 = 1. 8-12 19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. 8-12 20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30, 60, and 90 triangles and 45, 45, and 90 triangles. 8-12 21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. 8-12 22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. 414-418, 424 506, 507-513, 536 508-513, 515, 517-521, 536 499-505, 535 762-769, 770, 771-779, 780-787, 789, 790-797, 812-813 544-551, 553-558, 559-565, 566-567, 584-592, 595-596, 598, 604, 606 497, 799 693, 706, 714, 723, 731, 738 math812grsm.doc 6