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Geometry curriculum - first semester: Academic Algebra 2 – first semester
   
Essentials of Geometry Unit 1: Linear Programming
• Vocabulary & Symbolic Notation • Context: Linear Programming problem: “Manufacturing”
• Definition & Symbolic Notation • Linear Equations
• Distance Formula • Linear Inequalities
• Pythagorean Theorem • Graphing Equations / Inequalities
• Segment & Angle Addition Postulates • Systems of Equations / Inequalities
• Segment & Angle Bisectors • Constraints
• Midpoint Formula • Feasible Region
• Vertical Angles/Linear Pair • Objective
• Complementary & Supplementary Angles • Optimization
• Construction  
  Unit 2: Functions & Transformations
Plane Shapes & Polygons • Relation
• Identifying Plane Shapes • Function
• Classification and Properties of Special Quadrilaterals • Representation: graphical, mapping, algebraic
• Properties of Trapezoids and Kites • Domain / Range
• Angle measures in Polygons • Function Notation
  • Evaluating Functions
Area & Perimeter of Plane Shapes • Properties of Exponents
• Plane Shapes • Introduction to Foiling
• Perimeter of plane figures and Circumference of circles • Operations with Functions
• Area of Triangles & Special Quadrilaterals • Composition of Functions
• Area of Equilateral Triangles & Regular Polygons (Honors only) • Parent Functions
• Arc Length of Circles • Absolute Value
• Area of Sectors of Circles • Quadratic
• Areas of Composite Figures & Shaded Regions • Cubic
• Geometric Probability • Square Root
  • Cube Root
Surface Area & Volume • Reciprocal
• Defining Solids  
• Nets of solids Unit 3: Quadratic Functions
• Surface Areas of prisms, cylinders, pyramids, and cones • Vertex Form to Standard Form
• Volumes of prisms, cylinders, pyramids, and cones • Factoring
• Surface Areas and Volumes of a sphere • Graph analysis
  • Solve using Square Roots
Logic • Quadratic Formula and Discriminant
• Inductive & Deductive Reasoning • Vertex Formula
• Conditional, Counterexample, Inverse, Converse, Contrapositive; Biconditional statements • Applications of Quadratic Function
• Law of Detachment • Special Case: Quadratics with no real solutions
• Law of Syllogism  
• Simple Algebraic Proofs  
   
Parallel & Perpendicular Lines  
• Identifying pairs of lines and angles  
• Use parallel lines and transversals  
• Prove lines are parallel using angles  
• Slopes of parallel lines using coordinates  
• Proofs and slopes of perpendicular lines  
• Proving parallelograms