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Geometry Benchmarks |
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*These Benchmarks were revised in July 2010. References in black are to the 2001 SOL. References in red are to the 2009 SOL. A Guide for Parent Involvement
Note: Chapters referenced are from the adopted text, Glencoe: Geometry. These benchmarks apply to both the single and double blocked courses.
1st Nine Weeks Chapter 1: Points, Lines, Planes, and Angles (All Sections) Related SOLs: G.2 The student will use pictorial representations, including computer software, constructions, and coordinate methods to solve problems involving symmetry and transformation. This will include investigating and using formulas for finding distance, midpoint, and slope; investigating symmetry, and determining whether a figure is symmetric with respect to a line or a point; and determining whether a figure has been translated, reflected, or rotated. G.3 The student will solve practical problems involving complementary, supplementary, and congruent angles that include vertical angles, angles formed when parallel lines are cut by a transversal, and angles in polygons. G.11 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.12 The student will make a model of a three-dimensional figure from a two-dimensional drawing and make a two-dimensional representation of a three-dimensional object. Models and representations will include scale drawings, perspective drawings, blueprints, or computer simulations. Chapter 2: Reasoning and Proof (All Sections) Related SOLs: G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include identifying the converse, inverse, and contrapositive of a conditional statement; translating a short verbal argument into symbolic form, using Venn diagrams to represent set relationships, and using deductive reasoning, including the law of syllogism. G.3 (see above) G.4 The student will use the relationships between angles formed by two lines cut by a transversal to determine if two lines are parallel and verify, using algebraic and coordinate methods as well as deductive proofs. Chapter 3: Parallel and Perpendicular Lines (3.1-3.3, 3.4, 3.5-3.6) Add the constructions described on p 24 and on p 151, and have the students justify them. Related SOLs: G.2 (see above) G.3 (see above) G.4 (see above) G.12 (see above) 2nd Nine Weeks Chapter 4: Congruent Triangles (All Sections) Related SOLs: G.2 (see above) G.5 The student will investigate and identify congruence and similarity relationships between triangles; and prove two triangles are congruent or similar given information in the form of a figure or statement, using algebraic and coordinate as well as deductive proofs. G.8 The student will investigate and identify properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals; prove these properties of quadrilaterals using algebraic and coordinate methods as well as deductive reasoning; and use properties of quadrilaterals to solve practical problems. G.9 The student will use measures of interior and exterior angles of polygons to solve problems. Tessellations and tiling problems will be used to make connections to art, construction, and nature. Chapter 5: Relationships in Triangles (All Sections) Related SOLs: G.1 (see above) G.3 (see above) G.5 (see above) G.6 The student, given information concerning the lengths of sides and/or measures of angles, will apply the triangle inequality properties to determine whether a triangle exists and to order sides and angles. These concepts will be considered in the context of practical situations. Chapter 6: Proportions and Similarity (6.1-6.5) Related SOLs: G.2 (see above) G.5 (see above) G.9 (see above) G.12 (see above) G.14 The student will use proportional reasoning to solve practical problems, given similar geometric objects; and determine how changes in one dimension of an object affect area and/or volume of the object. 3rd Nine Weeks
Chapter 7: Right Triangles and Trigonometry (7.2-7.5) Related SOL: G.7 The student will solve practical problems involving right triangles by using the Pythagorean Theorem, properties of special right triangles and right triangle trigonometry. Solutions will be expressed in radical form or as decimal approximations. Chapter 8: Quadrilaterals (All Sections) Related SOLs: G.3 (see above) G.4 (see above) G.5 (see above) G.8 (see above) G.9 (see above) Chapter 9: Transformations (9.1-9.4, 9.5) Related SOLs: G.2 (see above) G.9 (see above) Chapter 10: Circles (10.1-10.7, 10.8) Related SOL: G.10 The student will investigate and solve practical problems involving circles, using properties of angles, arcs, chords, tangents, and secants to solve problems involving circles. Problems will include finding arc length and area of a sector, and may be drawn from applications of architecture, art, and construction. 4th Nine Weeks
Chapter 11: Areas of Polygons and Circles (All Sections) Related SOLs: G.8 (see above) G.10 (see above) G.14 (see above) Chapter 12: Surface Area (All Sections) Related SOLs: G.12 (see above) G.13 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. Chapter 13: Volume (13.1-13.4) Related SOLs: G.13 (see above) G.14 (see above) Review for SOL Test |