Compiled Unit 3 Curricular Sequence

1. Section 3.1: Pairs of Lines and Angles
   • Core Content: Formal definitions and notation for Parallel Lines, non-coplanar Skew Lines, Parallel Planes, and cutting Transversals. Includes structural identifying line/plane practice using a 3D solid prism model.
   • Axioms Covered: The fundamental Euclidean existence constraints—the Parallel Postulate and Perpendicular Postulate.
   • Practice Bundle
2. Section 3.2: Parallel Lines and Transversals
   • Core Content: Comprehensive tracking of interior and exterior geometric networks when parallel pathways are split.
   • Theorems Covered: Corresponding Angles Theorem (3.1), Alternate Interior Angles Theorem (3.2), Alternate Exterior Angles Theorem (3.3), and Consecutive Interior Angles Theorem (3.4).
   • Practice Bundle
3. Section 3.3: Proofs with Parallel Lines
   • Core Content: Exploring conditional proof inversions to show how specific angle dimension sets prove that lines are parallel.
   • Theorems Covered: Reversing standard axioms via the Corresponding Angles Converse, Alternate Interior Angles Converse, Alternate Exterior Angles Converse, and Consecutive Interior Angles Converse.
   • Practice Bundle
4. Section 3.4: Proofs with Perpendicular Lines
   • Core Content: Calculating the absolute shortest scalar path from an external point to a target boundary line, alongside the formal definitions and manual compass-and-straightedge construction steps for a Perpendicular Bisector.
   • Theorems Covered: Linear Pair Perpendicular Theorem (3.10), Perpendicular Transversal Theorem (3.11), and Lines Perpendicular to a Transversal Theorem (3.12).
   • Practice Bundle
5. Section 3.5: Equations of Parallel and Perpendicular Lines
   • Core Content: Geometric coordinate calculations covering directional vector paths (Directed Line Segments) and section interval partitioning via linear ratios (e.g., 3:2 or 4:1 partitioning).
   • Slope Rules: Deep dive into parallel slope equality constraints vs. perpendicular negative reciprocal properties.
   • Practice Bundle