Below topics are covered as part of Geometry course

Reasoning, Lines, and Transformations

G.1     Deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include

                           a)     identifying the converse, inverse, and contrapositive of a conditional statement;

                           b)     translating a short verbal argument into symbolic form; and

       c)      determining the validity of a logical argument.

G.2     Relationships between angles formed by two lines intersected by a transversal to

      a)         prove two or more lines are parallel; and

      b)         solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal.

G.3     Solve problems involving symmetry and transformation. This will include

                         a)     investigating and using formulas for determining distance, midpoint, and slope;

        b)     applying slope to verify and determine whether lines are parallel or perpendicular;

        c)     investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and

        d)     determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods.

Triangles

G.5     Given information concerning the lengths of sides and/or measures of angles in triangles, will solve problems, including practical problems.  This will include

      a)     ordering the sides by length, given angle measures;

      b)     ordering the angles by degree measure, given side lengths;

      c)     determining whether a triangle exists; and

      d)     determining the range in which the length of the third side must lie.

G.6    Given information in the form of a figure or statement, will prove two triangles are congruent.

G.7    Given information in the form of a figure or statement, will prove two triangles are similar.

G.8    Solve problems, including practical problems, involving right triangles.  This will include applying

a)      The Pythagorean Theorem and its converse;

b)      Properties of special right triangles; and

c)      Trigonometric ratios.

Polygons and Circles

G.9     Verify and use properties of quadrilaterals to solve problems, including practical problems.

G.10     Solve problems, involving angles of convex polygons.  This will include determining the

a)       Sum of the interior and/or exterior angles;

b)       Measure of an interior and/or exterior angle; and

c)       Number of sides of a regular polygon.

G.11     Solve problems, including practical problems, by applying properties of circles. This will include determining

a)       Angle measures formed by intersecting chords, secants, and/or tangents;

b)       Lengths of segments formed by intersecting chords, secants, and/or tangents;

c)       Arc length; and

d)       Area of a sector.

G.12      Solve problems involving equations of circles.

Three-Dimensional Figures

G.13      Surface area and volume of three-dimensional objects to solve practical problems.

G.14      The student will apply the concepts of similarity to two- or three-dimensional geometric figures.  This will include

a)       Comparing ratios between lengths, perimeters, areas, and volumes of similar figures;

b)       Determining how changes in one or more dimensions of a figure affect area and/or volume of the figure;

c)       Determining how changes in area and/or volume of a figure affect one or more dimensions of the figure; and

d)       Solving problems, including practical problems, about similar geometric figures.