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Geometry Pacing Guide (2008) First Six Weeks SOL G.3 Lines and Angles Second Six Weeks Estimated Time SOL 3 days G.5 Triangles and Logic The Student will solve practical problems involving complementary, supplementary and congruent angles that include vertical angles formed when parallel lines are cut by a transversal and angle in polygons G.1 Triangles and Logic 1 day The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include: Third Six Weeks Estimated Time SOL G.10 Polygons and Circles Estimated Time 5 days G.5a 3 days The student will investigate and identify congruence and similarity relationships between triangles The student will investigate and solve practical problems involving circles, using properties of angles, arcs, chords, tangents, and secants. Problems will include finding arc length and the area of G.5b 3 days a sector, and may be drawn from The student will prove two triangles are applications of art, construction, and congruent or similar, given information in nature. the form of a figure or statement, using algebraic and coordinate as well as deductive proofs. G.11 Lines and Angles 2 days G.2c 2 days G.1a 2 days Determining whether a figure has been Identifying the converse, inverse, and translated, reflected, or rotated. contrapositive of a conditional statement; G.1b 1 day G.7 Triangles and Logic 8 days Translating a short verbal argument into symbolic form; The student will solve practical problems involving right triangles by using the G.1c 1/2 day Pythagorean Theorem, properties of Using Venn diagrams to represent set special right triangles, and right triangle relationships; trigonometry. Solutions will be expressed in radical form or as decimal G.1d 1/2 day approximations. Using deductive reasoning, including the law of syllogism The student will construct a line segment congruent to a given line segment, the bisector of a line segment, a perpendicular to a given line from a point not on the line, a perpendicular to a given Line at a point on the line, the bisector of a given angle, and an angle congruent to a given angle. G.2b 1 day G.6 Triangles and Logic 2 days Investigating symmetry and determining whether a figure is symmetric with The student, given information respect to a line or a point concerning the lengths of sides and/or measures of angles, will apply the G.8 Polygons and Circles triangle inequality properties to determine whether a triangle exists and G.8a 4 days to order sides and angles. These The student will investigate and identify concepts will be considered in the context properties of quadrilaterals involving of practical situations. opposite sides and angles, consecutive sides and angles, and diagonals. G. 12 Three- Dimensional Figures 2 days G.8b 2 days The student will prove these properties of The student will make a model of a threequadrilaterals, using algebraic and dimensional figure from a twocoordinate methods as well as deductive dimensional drawing and make a tworeasoning. dimensional representation of a threedimensional object. Models and G.8c 2 days representations will include scale The student will use properties of drawings, perspective drawings, quadrilaterals to solve practical problems. blueprints, or computer simulations. G.13 Three- Dimensional Figures G.4 Lines and Angles 5 days 4 days The students will use the relationships between angles formed by two lines cut by a transversal to determine if two lines are parallel and verify algebraic and coordinate methods as well as deductive proofs. The student will use formulas for surface area and volume of three-dimensional objects to solve practical problems. Calculators will be used to find decimal approximations for results. G.9 Polygons and Circles 4 days G.14 Three-Dimensional Figures The student will use measures of interior and exterior angles of polygons to solve problems. Tessellations and tilting problems will be used to make connections to art, construction, and nature. G.2 Coordinate Relations and Transformations G.14a 2 days The student will use proportional reasoning to solve practical problems, given similar geometric objects. G.14b 3 days 2 days The student will determine how changes in one dimension of an object affect area The student will use pictorial and/or volume of the object. representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformations. This will include: G.2a 3 days Investigating and using formulas for finding distance, midpoint, and slope