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