01 · INTERSECTING LINES
Linear Pair & Vertically Opposite Angles
CORE THEOREMS
Angle Rules for Intersecting Lines
• Linear Pair Axiom: If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.
• Vertically Opposite Angles Theorem: If two lines intersect each other, then the vertically opposite angles are equal (∠AOC = ∠BOD and ∠AOD = ∠BOC).
02 · PARALLEL LINES AND TRANSVERSAL
Transversal Angle Pairs
When a transversal t intersects two parallel lines l ∥ m:
TRANSVERSAL AXIOMS
Parallel Lines Angle Relationships
1. Corresponding Angles are Equal: ∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, ∠4 = ∠8.
2. Alternate Interior Angles are Equal: ∠3 = ∠6, ∠4 = ∠5.
3. Consecutive Interior Angles are Supplementary (Sum = 180°): ∠3 + ∠5 = 180°, ∠4 + ∠6 = 180°.