Greater Nanticoke Area School District Geometry
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1 Greater Nanticoke Area School District Geometry Geometry emphasizes deductive and inductive reasoning and logic and written analysis of arguments to understand various types of proofs. The course includes coordinate and three dimensional geometry including right triangles, trigonometry and transformations of geometric figures. Standard Technology 2.3: is used Measurement to attain mastery and of standards. Estimation Standard 2.3 Measurement and Estimation CS A. Use units and tools to measure. 24. Use appropriate linear, square, and cubic units in making estimates and measurements A. English Units B. Metric Units 25. Use appropriate formulas and other tools to calculate area, volume, distance. 26. Use compass, protractor and ruler to measure segments, angles, and area. 27. Use appropriate formulas and ratios to measure geometric figures. CS2.3.11C. Determine relationships between linear, square and cubic measures. 30. Describe how changes in a linear dimension of an object affects its perimeter, area and volume. 31. Describe how changes in one of the measures of a figure affects the other measures. CS D. Demonstrate ability to produce measures with specified levels of precision 32. Make judgments in measurement situations about degree of precision needed and reasonableness of results. A. Rounding Standard 2.4: Mathematical Reasoning and Connections CS A. Use proofs to validate conjecture. 33. Define and differentiate inductive and deductive reasoning. 34. Identify the structure of geometric deductive reasoning (undefined term, postulates, theorems). 35. Use inductive reasoning to formulate theorems/hypotheses. 36. Use deductive reasoning to prove theorems and to formulate and prove conjectures. 37. Identify and interpret patterns and sequences to formulate conjectures. 38. Apply theorems, formulas, postulates, definitions and undefined terms in a logical manner to prove or disprove conjectures. 39. State and use the properties of equality and inequality. Geometry Standards 03/13/03 1
2 40. Write and interpret statements in if-then form. CS B. Construct valid arguments from stated facts. 41. Attack or defend a problem solution or procedure based on known facts. CS C. Determine the validity of an argument. 42. Determine if a solution is correct. 43. Use counter examples to test conjecture. 44. Use direct and indirect proofs to test validity. CS D. Use truth tables to reveal the logic of mathematical statements. 45. Write the negation of a statement. 46. Define a conditional statement and identify the hypothesis and conclusion. 47. Write conditional statements in if-then form. 48. Determine the converse of a conditional. 49. Determine the inverse of a conditional. 50. Determine the contrapositive of a conditional. 51. State the converse, inverse and contrapositive of the conditional. 52. Validate the truth or falsity of all the above elements. 53. Write a bi-conditional. CS E. Demonstrate mathematical solutions to problems across the curriculum. 54. Use algebraic formulas that apply to other disciplines 55. Use geometric formulas that apply to other disciplines. 56. Write a valid proof using a variety of reasoning strategies. B. Write proofs using a two-column format C. Write proofs using a paragraph format D. Write indirect proofs Standard 2.5 Mathematical Problem Solving and Communication CS2.5.11A: Solve non-routine and multi-step problems 57. Apply basic rules of real numbers in problem solving 58. Select and justify appropriate methods needed in solving multi-step problems. CS B. Use representations to communicate mathematically 59. Translate words into symbols and symbols into words. 60. Use appropriate mathematical terminology to communicate mathematically. CS C. Present procedures with precision in problem solving. 63. Develop a written and oral justification that presents results clearly, systematically, and succinctly. CS D. Summarize and evaluate results to problem solutions. 64. Write and describe a summary of results to determine validity Geometry Standards 03/13/03 2
3 Standard 2.9: Geometry CS A. Construct geometric figures using geometry tools Identify and name sets of points including line, plane, segment, ray 168. Draw representations of points, lines, segments, rays and planes, 169. Use straight edge, protractor and compass to construct geometric figures 170. Use geometry software to construct geometric figures 171. Construct congruent triangles using congruency postulates and theorems 172. Classify polygons according to sides and angles Identify, construct and use the definition of a circle and sets of points related to the circles. CS B. Prove that geometric figures are congruent or similar Identify corresponding parts of congruent and similar figures 176. Define and recognize congruent figures 177. Define and recognize similar figures 178. Use the distance formula to determine congruence or similarity 179. Use postulates and theorems to prove that two geometric figures and their corresponding parts are congruent Use postulates and theorems to prove that two geometric figures are similar, that corresponding angles of similar figures are congruent, and that corresponding sides of similar figures are proportional. CS C. Identify and prove the properties of quadrilaterals Recognize a quadrilateral as having four sides and four angles Recognize and name the parts of quadrilaterals. A. Sides B. Angles C. Vertices D. Consecutive sides E. Consecutive angles F. Opposite angles G. Opposite sides H. Diagonals 182. Recognize and identify special classes of quadrilaterals. A. Convex polygons. B. Regular polygons. C. Parallelograms. D. Trapezoids E. Concave polygons 184. Prove and apply theorems that state properties of parallelograms. A. Both pairs of opposite sides are parallel and congruent. B. Both pairs of opposite angles are congruent C. Diagonals of a parallelogram bisect each other D. Prove that if opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. Geometry Standards 03/13/03 3
4 E. The diagonal of any parallelogram forms two congruent triangles CS D. Identify corresponding parts in congruent triangles to solve problems Identify and describe the parts of triangles 186. Identify and label congruent triangles Use corresponding parts in congruent triangles to solve problems Apply congruency theorems for triangles to prove triangles congruent 190. Identify the specific congruency theorem that proves congruency CS E. Solve problems involving inscribed and circumscribed polygons Define and solve problems with inscribed polygons Define and solve problems with circumscribed polygons. CS F. Solve problems involving circles Identify and solve problems involving diameter, radius, chord and circumference Describe the relationship between tangent lines and circles, and solve problems involving tangents and circles Apply and solve problems involving arcs and angles of circles Apply theorems and solve problems that relate to chords of a circle Apply theorems and solve problems that relate to the tangents, secants, radii of a circle Describe the correlations among the equation of a circle, its center and radius length Discuss and solve problems involving congruent, similar and concentric circles. CS G. Solve problems using analytic geometry Use slope to determine if two lines are parallel or perpendicular 203. Determine coordinates of the vertices of polygons in a plane 204. Use coordinate geometry to verify conclusions regarding polygons 205. Solve problems involving quadrilaterals in a coordinate plane 206. Solve problems involving triangles in a coordinate plane. CS H. Construct a geometric figure and its image using various transformations 207. Investigate a variety of Transformations on Polygons in a coordinate plane: A. Reflections B. Translations C. Rotations D. Dilations. CS I. Model situations geometrically to formulate and solve problems Use the definitions of adjacent, vertical, complementary and supplementary angles, and linear pair to solve problems and write proofs Geometry Standards 03/13/03 4
5 210. Use the angle and segment addition postulate to solve problems and write proofs 211. Use the definition of angle bisector to solve problems and write proofs 212. Use the definitions of parallel lines, perpendicular lines, and perpendicular bisectors to solve problems and write proofs 213. Use the relationships that exist between special pairs of angles formed by parallel lines cut by a transversal to solve problems and write proofs 214. Use the measures of the interior and exterior angles of a convex polygon to solve problems 215. Use the properties of proportions to solve problems involving similar polygons 216. Use the properties of congruent and similar polygons to solve problems and write proofs 216B. Use appropriate formulas to find the sum of measures of the interior and exterior angles of a convex polygon, and to find the measure of each interior and each exterior angle of a regular polygon Use the definition and properties of parallelograms to solve problems and write proofs 218. Develop and use properties of rectangles, rhombi, and squares to solve problems and write proofs 219. Use the definition and properties of trapezoids and isosceles trapezoids to solve problems and write proofs 220. Use the relationships in a special right triangle to solve problems and write proofs. 220B. Use the geometric mean to solve problems involving right triangles. Standard 2.10: Trigonometry CS A. Identify, create, and solve practical problems involving triangles Use the Pythogorean Theorem to solve problems involving right triangles Define the six trigonometric ratios (i.e. functions): A. Sine B. Cosine C. Tangent D. Cotangent E. Secant F. Cosecant 226. Use the six trigonometric ratios (i.e. functions) to solve problems involving right triangles. Geometry Standards 03/13/03 5
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