GEOMETRY (Advanced) – Isosceles-Equilateral Triangle

Isosceles-Equilateral Triangle (AYT)

Learning Time: 4-12 hours

Content: Isosceles and equilateral triangles are covered at a more advanced level in the AYT curriculum, including angle bisector and side bisector relationships, trigonometric analysis, triangles in space, and complex problems. This topic supports the transition to analytic geometry. The current 2025 AYT curriculum also includes vectors and triangle centers (e.g., interior angle bisector centers).

• Isosceles Triangle Advanced Analysis:
  • Angle Bisector and Side Bisector Relationships
  • Trigonometric Relations (Sine, Cosine)
  • Isosceles Triangle in Space
• Equilateral Triangle Advanced Analysis:
  • Triangle Centers (Center of Gravity, Center of Interior Bisector)
  • Vector Symmetry Analysis
  • Complex Proofs
• Problem Solving and Proof:
  • Complex Triangle Problems
  • Geometric and Analytical Proofs
  • Applications in Space
• Applications:
  • Symmetry in Engineering Analysis
  • Trigons in Space Designs
  • Trigonometric Modeling
• Affecting Factors:
  • Side Lengths
  • Angle Measurements
  • Use of Coordinate System