• Geometry
     
    Please use the link below to access the classroom policies, expectations, and grading policy.
    Geometry Classroom Policies
     
    Course Description:

    Geometry is intended to be the second course in mathematics for high school students. During high school, students begin to formalize their geometry experiences from elementary and middle school, using more precise definitions to establish the validity of geometric conjectures through deduction, proof, or mathematical arguments. Over the years, students develop an understanding of the attributes and relationships of two- and three-dimensional geometric shapes that can be applied in diverse contexts.

     

    The concepts of congruence, similarity, and symmetry can be understood from the perspective of geometric transformations. Fundamental are the rigid motions: translations, rotations, reflections, and sequences of these, all of which are here assumed to preserve distance and angle measure reflections and rotations each explain a particular type of symmetry leading to insight into a figure’s attributes. Two geometric figures are defined to be congruent if there is a sequence of rigid motions that maps one figure onto the other. For triangles, congruence means that all corresponding pairs of sides and all corresponding pairs of angles are congruent. This leads to the triangle congruence criteria ASA, SAS, SSS, AAS and Hypotenuse-Leg (HL). Once these criteria are established using rigid motions, they can be used to prove theorems about triangles, quadrilaterals, and other geometric figures.

     

    Similarity transformations define similarity as a sequence of dilations and/or rigid motions that maps one figure onto another. Students formalize the similarity ideas of "same shape" and "scale factor" developed in the middle grades by establishing that similar triangles have all pairs of corresponding angles congruent and all corresponding pairs of sides proportional. These transformations lead to the criteria AA, SSS similarity, and SAS similarity for similar triangles.

     

    The definitions of sine, cosine, and tangent for acute angles are founded on right triangles and similarity, along with the Pythagorean Theorem and are fundamental in many mathematical situations. Radian measure will be introduced in Algebra II, along with the unit circle.

     

    Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area, and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line. They reason abstractly and quantitatively to model problems using volume formulas.

     

    Students prove and apply basic theorems about circles and study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students explain the correspondence between the definition of a circle and the equation of a circle written in terms of the distance formula, its radius, and coordinates of its center. Given an equation of a circle, students graph the circle in the coordinate plane and apply techniques for solving quadratic equations.