Sniper Mode: Visual Math

1. Lines & Angles

• Parallel Lines Rules:
  • Z-Rule: Alternate Interior Angles equal.
  • F-Rule: Corresponding Angles equal.
  • C-Rule: Co-Interior angles sum = 180 degree.
• Linear Pair: Angles on straight line sum 180.
• Vertically Opposite: X shape. Angles are equal.

2. Triangles (King of Geometry)

• Sum Property: A+B+C = 180.
• Exterior Angle: Equal to sum of two opposite interior angles.
• Centers:
  • Centroid (G): Median intersection. Divides median in 2:1.
  • Incenter (I): Angle bisector intersection. Equidistant from sides.
  • Circumcenter (O): Perpendicular bisector intersection. Equidistant from vertices.
  • Orthocenter (H): Altitude intersection.
• Congruency: SSS, SAS, ASA, RHS (Exact copy).
• Similarity: AAA, SSS, SAS (Same shape, different size). Ratio of areas = Ratio of side squares.

3. Circles

• Tangent: Touches at 1 point. Perpendicular to radius.
• Chord: Perpendicular from center bisects chord.
• Angle Property: Angle at center is double the angle at circumference.
• Cyclic Quadrilateral: Opposite angles sum = 180.