Segment A of Geometry teaches that spatial reasoning and visualization are ways to orient thinking about the physical world. Logical reasoning creates a higher level of thinking used throughout geometry. Congruence describes a special similarity relationship between objects and is a form of equivalence. Similarity relationships between objects are a form of proportional relationships.

Segment B of Geometry teaches that there are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Objects can be transformed in an infinite number of ways. Transformations can be described and analyzed mathematically. Circles have mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations. Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.

PRE-REQUISITES: Algebra recommended

ESTIMATED COMPLETION TIME: For both segments 32-36 weeks or approximately 125 – 135 hours

MAJOR TOPICS AND CONCEPTS — SEGMENT A

Geometry Foundations

  • Points, Lines, and Planes
  • Segments and Congruence
  • Angles and Measurement
  • Angle Pairs
  • Angle Bisectors and Segment Midpoints
  • Midpoint and Distance Formulas

Reasoning and Proof

  • Inductive Reasoning
  • Logic and Conditional Statements
  • Deductive Reasoning
  • Postulates, Diagrams, and Proof
  • Algebraic Proof
  • Proofs with Angle Pairs and Segments

Parallel Lines and Congruent Triangles

  • Identify Lines and Angles
  • Parallel Lines and Transversals
  • Prove Lines Parallel
  • Perpendicular Line Theorems
  • Introduction to Triangles
  • Congruence and Triangles
  • Prove Triangles Congruent
  • Isosceles and Equilateral Triangles

Relationships in Triangles and Similarity

  • Mid-segments and Perpendicular Bisectors
  • Angle Bisectors of Triangles
  • Medians and Altitudes
  • Inequalities and Triangles
  • Ratio, Proportion, and the Geometric Mean
  • Similar Polygons
  • Prove Triangles Similar
  • Proportionality Theorems

MAJOR TOPICS AND CONCEPTS — SEGMENT B

Right Triangles and Trigonometry

  • Pythagorean Theorem
  • Converse of the Pythagorean Theorem
  • Similar Right Triangles
  • Special Right Triangles
  • Sine, Cosine, and Tangent
  • Solve Right Triangles

Quadrilaterals and Transformations

  • Polygons and Parallelograms
  • Properties of Quadrilaterals
  • Trapezoids and Kites
  • Translations and Vectors
  • Reflections and Line Symmetry
  • Rotations and Rotational Symmetry
  • Dilations and Compositions

Circles

  • Introduction to Circles
  • Arc Measures
  • Chords
  • Inscribed Angles and Polygons
  • Angle Relationships
  • Segment Lengths of Circles
  • Graphing Circles

Geometric Measurement and Dimension

  • Arc Length and Sectors
  • Areas of Regular Polygons
  • Surface Area of Prisms and Cylinders
  • Surface Area of Pyramids and Cones
  • Volume of Prisms and Cylinders
  • Volume of Pyramids and Cones
  • Surface Area and Volume of Spheres
  • Similar Solids

LINKS TO FULL COURSE CURRICULUM MAPS

SEGMENT A

SEGMENT B