Geometry

Couse Overview

  • Introduction to Geometry: Concepts & Importance

  • Points, Lines, Planes, Segments, Rays, and Angles

  • Angle Types: Acute, Right, Obtuse, Straight

  • Geometric Notation, Symbols, Postulates, and Theorems

Reasoning & Proof

  • Logical Reasoning and Types of Proofs (Two-Column, Paragraph, Flowchart)

  • Proving Triangle Congruence and Similarity

  • Proving Angle Relationships and Properties

  • Proofs Involving Area, Perimeter, and Volume

Connections/Real-World Applications

  • Algebra and Geometry Connections

  • Geometry in Architecture, Art, Design, Engineering, and Mapping

  • Real-World Problem Solving Throughout the Course

Geometric Shapes & Properties

  • Exploration of Shapes and Figures

  • Congruence and Similarity

  • Properties and Classifications of Triangles and Polygons

  • Special Triangles (30-60-90, 45-45-90), Triangle Inequality Theorem

Transformations & Symmetry

  • Translations, Reflections, Rotations, Dilations

  • Properties of Transformations

  • Line and Rotational Symmetry

  • Composition of Transformations

  • Identifying Congruence with Transformations

Lines & Angles

  • Parallel & Perpendicular Lines

  • Transversals and Angle Relationships (Alternate Interior, Exterior, Corresponding)

  • Proving Lines Parallel

  • Coordinate Geometry with Lines (Slope, Equations)

Circles

  • Circle Terminology: Radius, Diameter, Chords, Tangents, Secants

  • Central and Inscribed Angles, Arcs

  • Tangent and Chord Theorems

  • Area, Circumference, Sector Area, and Arc Length

Area, Perimeter, Surface Area/Volume

  • Area & Perimeter of Triangles, Quadrilaterals, Polygons

  • Surface Area & Volume of Prisms, Cylinders, Pyramids, Cones, Spheres

  • Nets and 3D Shapes

  • Applications in Design and Construction

Coordinate Geometry

  • Cartesian Plane: Plotting and Graphing

  • Distance and Midpoint Formulas

  • Equations of Lines and Graphing Figures

  • Applications in Computer Graphics, Urban Planning

Trigonometry & Geometric Probability

  • Trigonometric Ratios: Sine, Cosine, Tangent

  • Solving Right Triangles; Law of Sines & Cosines

  • The Unit Circle

  • Geometric Probability: Length, Area, Volume

  • Real-World Trigonometry & Probability Applications