• GEOMETRY CLASS OBJECTIVES

    The mathematics learning experience in Geometry centers on Reasoning and Logic, Two and Three-Dimensional Shapes including Circles, and Right Triangle Trigonometry.  Students have been introduced to most common of these topics as early as 4th grade but mainly in 7th grade and Pre-Algebra.  Students in this course will extend their knowledge about basic shapes of finding surface area and volume of uncommonfigures to include logical reasoning, problem-based activities, and the use of trigonometric ratios. Real world applications and problem-solving strategies will be integrated throughout the course.

    The following is the content that will be covered in PreAP Geometry. 

    (Changes may be made according to the school schedule, considering school activities and possible snow days.)

    UNIT 1 UNIT 2 UNIT 3
    Points, Lines, and Planes  Conditional Statements Pairs of Lines and Angles
    Measuring and Constructing Segments  Inductive and Deductive Reasoning Parallel Lines and Transversals
    Using Midpoint and Distance Formulas  Postulates and Diagrams Proofs with Parallel Lines
    Perimeter and Area in the Coordinate Plane  Algebraic Reasoning Proofs with Perpendicular Lines
    Measuring and Constructing Angles  Proving Statements about Segments and Angles Equations of Parallel and Perpendicular Lines
    Describing Pairs of Angles  Proving Geometric Relationships  

     

    UNIT 4 UNIT 5 UNIT 6
    Translations  Angles of Triangles Perpendicular and Angle Bisectors
    Reflections  Congruent Polygons Bisectors of Triangles
    Rotations  Proving Triangle Congruence by SAS Medians and Altitudes of Triangles
    Congruence and Transformations  Equilateral and Isosceles Triangles Points of Concurrency
    Dilations  Proving Triangle Congruence by SSS The Triangle Midsegment Theorem
    Similarity and Transformations  Proving Triangle Congruence by ASA and AAS Indirect Proof and Inequalities in One Triangle
      Using Congruent Triangles Inequalities in Two Triangles
      Coordinate Proofs  

     

    UNIT 7 UNIT 8 UNIT 9
    Angles of Polygons  Similar Polygons The Pythagorean Theorem
    Properties of Parallelograms  Proving Triangle Similarity by AA Special Right Triangles
    Proving That a Quadrilateral is a Parallelogram  Proving Triangle Similarity by SSS and SAS Very Special Right Triangles
    Properties of Special Parallelograms  Proportionality Theorems Similar Right Triangles
    Properties of Trapezoids and Kites   The Cosine, Sine and Tangent Ratios
        Solving Right Triangles
        Law of Sines and Law of Cosines

     

    UNIT 10 UNIT 11
    Writing Equations of Bounded Regions  Lines and Segments That Intersect Circles
    Graphing and Finding Area of Bounded Regions  Finding Arc Measures
    Systems of Linear Equations and Bounded Area  Using Chords
    Circumference and Arc Length  Inscribed Angles and Polygons
    Areas of Circles and Sectors  Angle Relationships in Circles
    Areas of Polygons  Segment Relationships in Circles
    Three-Dimensional Figures  Circles in the Coordinate Plane
    Surface Areas of Prisms and Cylinders  
    Surface Areas of Pyramids and Cones  
    Surface Areas of Spheres  
    Volumes of Prisms and Cylinders  
    Volumes of Pyramids  
    Volumes of Cones  
    Volumes of Spheres