Mathematics Standards of Learning
Reprinted with permission from:

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Intro | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Pre Algebra | Algebra I | Geometry

Geometry

This set of standards includes emphasis on two- and three-dimensional reasoning skills, coordinate and transformational geometry, and the use of geometric models to solve problems. A variety of applications and some general problem-solving techniques should be used to implement these standards, including algebraic skills.

• G.1 The student will recognize the three undefined terms "point", "line", and "plane", and their symbols, and be able to use these to define other terms such as "space", "ray", "angle" and so on.
• G.2 The student will know the five major "existence" postulates about points lines and planes:
  • 1) A line contains at least two points, a plane contains at least three points not all on one line; a space contains at least four points not all on one plane;
  • 2) There is exactly one line through two points;
  • 3) There is exactly one plane through three points not on one line;
  • 4) If two points lie in a plane, then the line joining them lies in that plane;
  • 5) If two planes intersect, their intersection is a line.
• G.3 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;
  • diagramming arguments involving quantifiers (all, no, none, some), using Venn diagrams;
  • using valid forms of deductive reasoning, including the law of syllogism; and
  • recognizing logical errors in faulty arguments.
• G.4 The student will use pictorial representations and coordinate methods to solve problems involving symmetry and transformation. This will include
  • using formulas for finding distance, midpoint, and slope;
  • investigating and determining whether a figure is symmetric with respect to a line or point; and
  • determining whether a figure has been translated, reflected, or rotated.
• G.5 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. The student will know and use the Exterior Angle Theorem to find angle measures in triangles.
• G.6 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.
• G.7 The student will
  • 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 be able to state and be able to use the Triangle Inequality Theorem. Given information concerning the lengths of sides and/or measures of angles, the student 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.
• G.9 The student will solve practical problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry. Because special right triangles and their properties recur, the student will commit to memory the side ratios of special right triangles and use them to solve triangle problems.
• G.10 The student will
  • identify properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals;
  • prove these properties of quadrilaterals using algebraic and coordinate as well as deductive proofs;
  • use properties of quadrilaterals to solve practical problems.
• G.11 The student will understand the meaning of the term "regular polygon" and be able to determine the measures of the interior and exterior angles of regular polygons. In addition, the student will use measures of interior and exterior angles of polygons to solve problems.
• G.12 The student will use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles. Problems will include finding the area of a sector and doing constructions. At the honors level, this will include constructing inscribed or circumscribed circles given a triangle; locating the center of a circle; and constructing the tangent to a circle from a point on the circle and from a point not on the circle.
• G.13 The student will construct, using a compass and straightedge, 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, an angle congruent to a given angle, and a line parallel to a given line from a point not on the line.
• G.14 The student will
  • understand the meaning of 'locus' and be able to describe and draw the locus of points satisfying a given condition;
  • solve locus problems using constructions. In particular he or she will be able to locate the circumcenter, incenter, orthocenter and centroid of a given triangle using constructions previously learned.
• G.15 The student will use formulas for surface area and volume of three-dimensional objects to solve practical problems.
• G.16 The student, given similar geometric objects, will use proportional reasoning to solve practical problems; investigate relationships between linear, square, and cubic measures; and describe how changes in one of the measures of the object affect the others.