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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
Standard
2.3:
Measurement
Estimation
geometric figures.
Technology
is used
to attain masteryand
of standards.
Standard 2.3 Measurement and Estimation
CS 2.3.11A. 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 2.3.11D. 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 2.4.11A. 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
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40. Write and interpret statements in if-then form.
CS 2.4.11B. Construct valid arguments from stated facts.
41. Attack or defend a problem solution or procedure based on known facts.
CS 2.4.11C. 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 2.4.11D. 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 2.4.11E. 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 2.5.11B. Use representations to communicate mathematically
59. Translate words into symbols and symbols into words.
60. Use appropriate mathematical terminology to communicate mathematically.
CS 2.5.11C. Present procedures with precision in problem solving.
63. Develop a written and oral justification that presents results clearly,
systematically, and succinctly.
CS 2.5.11D. Summarize and evaluate results to problem solutions.
64. Write and describe a summary of results to determine validity
Geometry Standards
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Standard 2.9: Geometry
CS 2.9.11A. Construct geometric figures using geometry tools.
167. 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.
173. Identify, construct and use the definition of a circle and sets of points related
to the circles.
CS 2.9.11B. Prove that geometric figures are congruent or similar.
175. 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.
179. 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 2.9.11C. Identify and prove the properties of quadrilaterals.
180. Recognize a quadrilateral as having four sides and four angles.
181. 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.
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E. The diagonal of any parallelogram forms two congruent triangles
CS 2.9.11D. Identify corresponding parts in congruent triangles to solve problems.
185. Identify and describe the parts of triangles
186. Identify and label congruent triangles.
187. Use corresponding parts in congruent triangles to solve problems.
189. Apply congruency theorems for triangles to prove triangles congruent
190. Identify the specific congruency theorem that proves congruency
CS 2.9.11E. Solve problems involving inscribed and circumscribed polygons.
191. Define and solve problems with inscribed polygons.
192. Define and solve problems with circumscribed polygons.
CS 2.9.11F. Solve problems involving circles.
193. Identify and solve problems involving diameter, radius, chord and
circumference.
194. Describe the relationship between tangent lines and circles, and solve
problems involving tangents and circles.
195. Apply and solve problems involving arcs and angles of circles.
196. Apply theorems and solve problems that relate to chords of a circle.
197. Apply theorems and solve problems that relate to the tangents, secants, radii
of a circle.
198. Describe the correlations among the equation of a circle, its center and radius
length.
199. Discuss and solve problems involving congruent, similar and concentric
circles.
CS 2.9.11G. Solve problems using analytic geometry.
202. 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 2.9.11H. 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 2.9.11I. Model situations geometrically to formulate and solve problems.
209. Use the definitions of adjacent, vertical, complementary and supplementary
angles, and linear pair to solve problems and write proofs
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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.
217. 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 2.10.11A. Identify, create, and solve practical problems involving triangles.
224. Use the Pythogorean Theorem to solve problems involving right triangles.
225. 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.
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