Prentice Hall: UCSMP Geometry '1998 Correlated to California Standards for Mathematics Geometry (Grades 8-12)

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Hilda Lyons
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1 California Standards for Mathematics Geometry (Grades 8-12) 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. 1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. 2.0 Students write geometric proofs, including proofs by contradiction. SE/TE: The Need for Undefined Terms, 35-40; Postulates for Euclidean Geometry, 41-45; Betweenness and Distance, 46-51; The Need for Definitions, 64-68; If-Then Statements, 69-76; Converses, 76-80; Conjectures, ; The Logic of Making Conclusions, ; see also Self-Test and Review, 56-61, , TE: Chapter Planners for teaching, resources, and assessment, 4A-4D, 62A-62D, 620A-620D TR: Lesson and Answer Masters: 1-6, 1-7, 1-8, 1-R, 2-1, 2-2, 2-3, 2-8, 2-R, 11-1, 11-R; Teaching Aids: 2, 3, 9, 10, 11, 13, 20, 143, 146; Activity Kits: 3; Technology Sourcebook: Comp 2, 4; Assessment Sourcebook: Quiz 1-6, 2-3, 11-4; Chapter Tests 1, 2, 11; Video Segment: 2-2 SE/TE: One-Step Proof Arguments, ; Two-Column Proofs, ; Indirect Proof, ; Proofs with Coordinates, ; and proofs throughout the following standards; see also Self-Test and Review, , , TE: Chapter Planners for teaching, resources, and assessment, 122A- 122D, 242A-242D, 620A-620D TR: Lesson and Answer Masters: 3-5, 3-R, 5-4, 5-R, 11-4, 11-5, 11-R; Teaching Aids: 4, 23, 29, 60, 68, 105, 144, 150, 151, 152; Technology Sourcebook: Calc 3; Assessment Sourcebook: Quiz 3-6, 5-6, 11-4, 11-7; Chapter Tests 3, 5, 11; Technology Software: GeoExplorer 11-4; and other resources related to proof correlated to the following standards 1

2 3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. SE/TE: The Need for Definitions, 64-68; If-Then Statements, 69-76; Converses, 76-80; Good Definitions, 81-86; Unions and Intersections of Figures, 87-93; Conjectures, ; The Logic of Making Conclusions, ; Negations, ; Ruling Out Possibilities, ; see also Self-Test and Review, , TE: Chapter Planners for teaching, resources, and assessment, 62A-62D, 620A-620D TR: Lesson and Answer Masters: 2-1, 2-2, 2-3, 2-4, 2-5, 2-8, 2-R, 11-1, 11-2, 11-3, 11-R; Teaching Aids: 4, 11, 12, 14, 15, 16, 17, 104, 143, 146, 147, 148, 149; Activity Kits: 3; Technology Sourcebook: Comp 2; Assessment Sourcebook: Quiz 2-3, 2-6, 11-4; Chapter Tests 2, 11; Technology Software: Spreadsheet 2-2; Video Segment: 2-2 2

3 4.0 Students prove basic theorems involving congruence and similarity. SE/TE: When Are Figures Congruent?, ; Corresponding Parts of Congruent Figures, ; Congruence and Equality, ; One-Step Congruence Proofs, ; Proofs Using Transitivity, ; Triangle Congruence Theorems, ; The SSA Condition and HL Congruence, ; Similar Figures, ; The Fundamental Theorem of Similarity, ; see also Self-Test and Review, , , TE: Chapter Planners for teaching, resources, and assessment, 182A- 182D, 242A-242D, 684A-684D TR: Lesson and Answer Masters: 4-8, 4-R, 5-1, 5-2, 5-3, 5-4, 5-R, 12-5, 12-6, 12-R; Teaching Aids: 35, 38, 59, 60, 62, 63, 64, 65, 66, 67, 68, 105, 158, 159, 169, 170; Activity Kits: 25; Assessment Sourcebook: Quiz 5-3, 5-6; Chapter Tests 4, 5, 12; Video Segment:

4 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. 6.0 Students know and are able to use the triangle inequality theorem. SE/TE: Corresponding Parts of Congruent Figures, ; Proofs Using Reflections, ; Triangle Congruence Theorems, ; Proofs Using Triangle Congruence Theorems, ; Overlapping Triangles, ; The SSA Condition and HL Congruence, ; Similar Figures, ; The Fundamental Theorem of Similarity, ; The SSS Similarity Theorem, ; The AA and SAS Similarity Theorems, ; The Side-Splitting Theorem, ; Similarity in Right Triangles, 758; see also Self- Test and Review, , , , TE: Chapter Planners for teaching, resources, and assessment, 242A- 242D, 362A-362D, 684A-684D, 736A-736D TR: Lesson and Answer Masters: 5-1, 5-5, 5-R, 7-2, 7-3, 7-4, 7-5, 7-R; 12-5, 12-6, 12-R, 13-1, 13-2, 13-3, 13-R; Teaching Aids: 59, 60, 62, 63, 64, 65, 69, 87, 88, 90, 91, 92, 93, 94, 105, 158, 159, 169, 170, 171, 174, 175, 176; Activity Kits: 16, 25, 26; Technology Sourcebook: 13; Assessment Sourcebook: Quiz 5-3, 5-6, 7-3, 7-6, 13-3; Chapter Tests 5, 7, 12, 13; Technology Software: GeoExplorer 7-2, 13-1, 13-2, 13-3; Video Segment: 12-6 SE/TE: Using an Automatic Drawer: The Triangle Inequality, ; see also Self-Test and Review, TE: Chapter Planner for teaching, resources, and assessment, 62A-62D TR: Lesson and Answer Masters: 2-7, 2-R; Teaching Aids: 13; Activity Kits: 5; Technology Sourcebook: Comp 3; Assessment Sourcebook: Chapter Test 2; Technology Software: GeoExplorer 2-7 4

5 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. SE/TE: Parallel Lines, ; Proofs Using Transitivity, ; Auxiliary Figures and Uniqueness, ; Sums of Angle Measures in Polygons, ; Reflection-Symmetric Figures, ; Types of Quadrilaterals, ; Conjectures about Quadrilaterals, 322; Properties of Kites, ; Properties of Trapezoids, ; Properties of Parallelograms, ; Sufficient Conditions for Parallelograms, ; Arc Length and Circumference, ; Proofs with Coordinates, ; Equations for Circles, ; see also Self-Test and Review, , , , , , TE: Chapter Planners for teaching, resources, and assessment, 122A- 122D, 242A-242D, 298A-298D, 362A-362D, 434A-434D, 620A- 620D TR: Lesson and Answer Masters: 3-6, 3-R, 5-4, 5-6, 5-7, 5-R, 6-1, 6-3, 6-4, 6-5, 6-R, 7-7, 7-8, 7-R, 8-7, 8-R, 11-5, 11-7, 11-R; Teaching Aids: 4, 23, 30, 60, 61, 67, 68, 70, 71, 72, 73, 74, 76, 77, 79, 80, 81, 89, 96, 97, 98, 99, 103, 144, 145, 153; Activity Kits: 11, 12, 13; Technology Sourcebook: Comp 5, 11, 12, 17; Assessment Sourcebook: Quiz 3-6, 5-6, 6-3, 6-6, 11-7; Chapter Tests 3, 5, 6, 7, 8, 11; Technology Software: GeoExplorer 5-7, 6-3, 8-7; Video Segment: 6-3 5

6 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. SE/TE: Perimeter Formulas, ; Fundamental Properties of Area, ; Areas of Irregular Regions, ; Areas of Triangles, ; Areas of Trapezoids, ; Arc Length and Circumference, ; Estimating the Area of a Circle, 479; The Area of a Circle, ; Projects, ; Surface Areas of Prisms and Cylinders, ; Lateral Area of Regular Pyramids, 569; Surface Areas of Pyramids and Cones, ; Fundamental Properties of Volume, ; Multiplication, Area, and Volume, ; Volumes of Prisms and Cylinders, ; Organizing Formulas, ; Volumes of Pyramids and Cones, ; The Volume of a Sphere, ; The Surface Area of a Sphere, ; Projects, ; More Work with Vectors and Area, ; see also Self- Test and Review, , , TE: Chapter Planners for teaching, resources, and assessment, 434A- 434D, 562A-562D, 736A-736D TR: Lesson and Answer Masters: 8-1, 8-2, 8-3, 8-4, 8-5, 8-7, 8-8, 8-R, 10-1, 10-2, 10-3, 10-4, 10-5, 10-6, 10-7, 10-8, 10-9, 10-R, 13-8, 13-R; Teaching Aids: 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 114, 115, 131, 132, 133, 134, 135, 137, 138, 139, 141, 173; Activity Kits: 18, 22; Technology Sourcebook: 17, 18, 20, 21; Assessment Sourcebook: Quiz 8-3, 10-3, 10-6; Chapter Tests 8, 10, 13; Technology Software: GeoExplorer 8-7, 8-8, 10-1, 10-4; Video Segments: 8-8, 10-1,

7 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 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. SE/TE: Surface Areas of Prisms and Cylinders, ; Surface Areas of Pyramids and Cones, ; Volumes of Prisms and Cylinders, ; Organizing Formulas, ; Volumes of Pyramids and Cones, ; The Volume of a Sphere, ; The Surface Area of a Sphere, ; Projects, ; see also Self-Test and Review, TE: Chapter Planner for teaching, resources, and assessment, 562A-562D TR: Lesson and Answer Masters: 10-1, 10-2, 10-5, 10-6, 10-7, 10-8, 10-9, 10-R; Teaching Aids: 131, 132, 133, 134, 135, 137, 138, 139, 141, 142; Technology Sourcebook: 20, 21; Assessment Sourcebook: Quiz 10-3, 10-6; Chapter Tests 10; Technology Software: GeoExplorer 10-1; Video Segment: 10-1 SE/TE: Areas of Irregular Regions, ; Areas of Triangles, ; Areas of Trapezoids, ; The Area of a Circle, ; Projects, ; More Work with Vectors and Area, ; see also Self-Test and Review, , , TE: Chapter Planners for teaching, resources, and assessment, 434A- 434D, 736A-736D TR: Lesson and Answer Masters: 8-3, 8-4, 8-5, 8-8, 8-R, 13-8, 13-R; Teaching Aids: 102, 103, 104, 105, 107, 108, 109, 110, 111, 114, 115, 116, 173; Technology Sourcebook: 18; Assessment Sourcebook: Quiz 8-3, 8-6; Chapter Tests 8, 13; Technology Software: GeoExplorer 8-8; Video Segment: 8-8 7

8 11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. SE/TE: Perimeter Formulas, ; Fundamental Properties of Area, ; Arc Length and Circumference, ; Fundamental Properties of Volume, ; Multiplication, Area, and Volume, ; Organizing Formulas, ; see also Self-Test and Review, , TE: Chapter Planners for teaching, resources, and assessment, 434A- 434D, 562A-562D TR: Lesson and Answer Masters: 8-1, 8-2, 8-7, 8-R, 10-3, 10-4, 10-6, 10-R; Teaching Aids: 101, 103, 104, 105, 106, 131, 132, 139; Activity Kits: 18, 22; Technology Sourcebook: 18, 20, 21; Assessment Sourcebook: Quiz 8-3, 10-3, 10-6; Chapter Tests 8, 10; Technology Software: GeoExplorer 8-7, 10-4, Spreadsheet 10-4 SE/TE: Polygons, ; The Triangle Inequality, ; Sums of Angle Measures in Polygons, ; Isosceles Triangles, ; Types of Quadrilaterals, ; Conjectures about Quadrilaterals, 322; Properties of Kites, ; Properties of Trapezoids, ; Regular Polygons, ; Regular Polygons and Schedules, ; Constructing Quadrilaterals, 352; see also Self-Test and Review, , , TE: Chapter Planners for teaching, resources, and assessment, 62A-62D, 242A-242D, 298A-298D TR: Lesson and Answer Masters: 2-6, 2-7, 2-R, 5-7, 5-R, 6-2, 6-3, 6-4, 6-5, 6-7, 6-8, 6-R; Teaching Aids: 13, 18, 19, 61, 72, 73, 74, 75, 79, 80, 81, 82, 83, 85, 86; Activity Kits: 4, 5, 11, 13; Technology Sourcebook: Comp 3, 11, 12; Assessment Sourcebook: Quiz 2-6, 6-3, 6-6; Chapter Tests 2, 5, 6; Technology Software: GeoExplorer 2-7, 5-7, 6-3; Video Segment: 6-3 8

9 13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. SE/TE: Properties of Angles, ; Sums of Angle Measures in Polygons, ; Properties of Trapezoids, ; see also Self- Test and Review, , , TE: Chapter Planners for teaching, resources, and assessment, 122A- 122D, 242A-242D, 298A-298D TR: Lesson and Answer Masters: 3-3, 3-R, 5-7, 5-R, 6-5, 6-R; Teaching Aids: 2, 28, 61, 72, 74, 82, 83; Activity Kits: 11; Technology Sourcebook: Comp 11; Assessment Sourcebook: Quiz 3-3; Chapter Tests 3, 5, 6; Technology Software: GeoExplorer Students prove the Pythagorean theorem. SE/TE: The Pythagorean Theorem, ; see also Self-Test and Review, TE: Chapter Planner for teaching, resources, and assessment, 434A-434D TR: Lesson and Answer Masters: 8-6, 8-R; Teaching Aids: 103, 113; Activity Kits: 19; Technology Sourcebook: 16; Assessment Sourcebook: Quiz 8-6; Chapter Tests 8; Technology Software: GeoExplorer Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. SE/TE: The Pythagorean Theorem, ; The Distance Formula, ; see also Self-Test and Review, , TE: Chapter Planners for teaching, resources, and assessment, 434A- 434D, 620A-620D TR: Lesson and Answer Masters: 8-6, 8-R, 11-6, 11-R; Teaching Aids: 103, 113; Activity Kits: 19; Technology Sourcebook: 16; Assessment Sourcebook: Quiz 8-6; Chapter Tests 8; Technology Software: GeoExplorer 8-6 9

10 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 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. SE/TE: Drawing Parallel and Perpendicular Lines, ; Constructions, 172; Circle Constructions, 262, 272, 275; Investigating Perpendicular Bisectors, 269; Angle Bisectors, Medians, and Perpendicular Bisectors of a Triangle, 308; Constructing Quadrilaterals, 352; Drawing Triangles, ; see also Self-Test and Review, , TE: Chapter Planners for teaching, resources, and assessment, 122A- 122D, 362A-362D TR: Lesson and Answer Masters: 3-8, 3-R, 5-4, 5-5, 6-2, 7-1, 7-R; Teaching Aids: 4, 23, 87; Activity Kits: 7, 15; Technology Sourcebook: Comp 5, 6; Assessment Sourcebook: Quiz 7-3; Chapter Tests 3, 7; Technology Software: Spreadsheet 3-8; Video Segment: 3-8 SE/TE: Ordered Pairs as Points, 17-23; Proofs with Coordinates, , The Distance Formula, ; Equations for Circles, ; Means and Midpoints, ; Three-Dimensional Coordinates, , 676; The Transformation S k, ; Size Changes, ; Properties of Size Changes, ; see also Self-Test and Review, 56-61, , TE: Chapter Planners for teaching, resources, and assessment, 4A-4D, 620A-620D, 684A-684D TR: Lesson and Answer Masters: 1-3, 1-R, 11-5, 11-6, 11-7, 11-8, 11-9, 11-R, 12-1, 12-2, 12-3, 12-R; Teaching Aids: 1, 4, 105, 144, 145, 153, 154, 156, 157, 160, 161, 162, 163, 164; Activity Kits: 23, 24; Technology Sourcebook: 23, 24; Assessment Sourcebook: Quiz 1-3, 11-7, 12-4; Chapter Tests 1, 11, 12; Technology Software: GeoExplorer 11-8, 12-2; Video Segment:

11 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 = 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 Students know and are able to use angle and side relationships in problems with special right triangles, such as triangles and triangles. SE/TE: The Tangent of an Angle, ; The Sine and Cosine Ratios, ; More Work with Vectors and Area, ; Projects, ; see also Self-Test and Review, TE: TR: Chapter Planner for teaching, resources, and assessment, 736A-736D Lesson and Answer Masters: 13-6, 13-7, 13-8, 13-R; Teaching Aids: 4, 105, 172, 173, 180; Activity Kits: 28; Technology Sourcebook: 27; Assessment Sourcebook: Quiz 13-6; Chapter Tests 13; Technology Software: GeoExplorer 13-6; Video Segment: 13-7 SE/TE: The Tangent of an Angle, ; The Sine and Cosine Ratios, ; see also Self-Test and Review, TE: Chapter Planner for teaching, resources, and assessment, 736A-736D TR: Lesson and Answer Masters: 13-6, 13-7, 13-R; Teaching Aids: 4, 172, 180; Activity Kits: 28; Technology Sourcebook: 27; Assessment Sourcebook: Quiz 13-6; Chapter Tests 13; Technology Software: GeoExplorer 13-6; Video Segment: 13-7 SE/TE: Special Right Triangles, ; see also Self-Test and Review, TE: Chapter Planner for teaching, resources, and assessment, 736A-736D TR: Lesson and Answer Masters: 13-5, 13-R; Teaching Aids: 172, 179; Activity Kits: 27; Technology Sourcebook: 27; Assessment Sourcebook: Quiz 13-6; Chapter Tests 13; Technology Software: GeoExplorer

12 21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. SE/TE: Regular Polygons and Schedules, ; Regular Polygons and Unit Circles, 790; Chord Length and Arc Measurement, ; The Inscribed Angle Theorem, ; Locating the Center of a Circle, ; Angles Formed by Chords and Secants, ; Tangents to Circles and Spheres, ; Angles Formed by Tangents, ; Lengths of Chords, Secants, and Tangents, ; Circles Associated with Triangles, 853; Japanese Temple Geometry Theorems, 854; see also Self-Test and Review, , TE: Chapter Planners for teaching, resources, and assessment, 298A- 298D, 798A-798D TR: Lesson and Answer Masters: 6-8, 6-R, 14-1, 14-2, 14-3, 14-4, 14-5, 14-6, 14-7, 14-R; Teaching Aids: 75, 181, 182, 183, 185, 186, 187, 188, 189, 190; Activity Kits: 29, 30; Technology Sourcebook: Comp 25; Assessment Sourcebook: Quiz 14-3, 14-6; Chapter Tests 6, 14; Technology Software: GeoExplorer 14-1, 14-6; Video Segment:

13 22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. SE/TE: Arcs and Rotations, ; Reflecting Points, ; Reflecting Figures, ; Miniature Golf and Billiards, ; Composing Reflections over Parallel lines, ; Composing Reflections over Intersecting Lines, ; Translations and Vectors, ; Isometries, ; When Are Figures Congruent?, ; Projects, ; Proofs Using Reflections, ; Reflections-Symmetric Figures, ; Rotation Symmetry, ; Reflection Symmetry in Space, ; Viewing Solids and Surfaces, ; see also Self-Test and Review, , , , , TE: Chapter Planners for teaching, resources, and assessment, 122A- 122D, 182A-182D, 242A-242D, 298A-298D, 494A-494D TR: Lesson and Answer Masters: 3-2, 3-R, 4-1, 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7, 4-8, 4-R, 5-5, 5-R, 6-1, 6-6, 6-R, 9-6, 9-7, 9-R; Teaching Aids: 4, 21, 26, 27, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 69, 73, 75, 76, 77, 84, 119, 120, 125, 126; Activity Kits: 6, 8, 9, 10, 12, 14; Technology Sourcebook: Comp 7, 8, 9, 10; Assessment Sourcebook: Quiz 3-3, 4-3, 4-6, 5-6, 6-3, 6-6, 9-7; Chapter Tests 3, 4, 5, 6, 8; Technology Software: GeoExplorer 4-2, 4-3, 4-4, 4-5, 4-6; Video Segment:

Florida Mathematics Standards for Geometry Honors (CPalms # )

Florida Mathematics Standards for Geometry Honors (CPalms # ) A Correlation of Florida Geometry Honors 2011 to the for Geometry Honors (CPalms #1206320) Geometry Honors (#1206320) Course Standards MAFS.912.G-CO.1.1: Know precise definitions of angle, circle, perpendicular