GEOMETRY (Advanced) – Congruence and Similarity

Congruence and Similarity (AYT)

Learning Time: 4-12 hours

Content: Congruence is expanded in the AYT curriculum with more complex shapes (quadrilaterals, polygons) and analytical methods. This topic includes the use of trigonometry and coordinate geometry in congruence proofs. The current 2025 AYT curriculum also includes congruence in space and vector analysis. Similarity is addressed at an advanced level in the AYT curriculum, including ratio-proportion calculations, trigonometric similarity, similarity in space, and complex problems. This topic supports the transition to analytical geometry. The current 2025 AYT curriculum also includes vectors and polygon similarity.

• Advanced Similarity:
  • Similarity in Polygons
  • Similarity in Space
  • Ratio-Proportion Calculations
• Trigonometric Similarity:
  • Similarity with Sine and Cosine
  • Area Ratio (k²)
  • Volume Ratio (k³)
• Problem Solving and Proof:
  • Complex Similarity Problems
  • Geometric Proof Techniques
  • Vector Similarity Analysis
• Applications:
  • Scaling in Engineering
  • Similarity Analysis in Space
  • Trigonometric Modeling
• Affecting Factors:
  • Ratio Changes
  • Shape Complexity
  • Using Coordinates
• Advanced Congruence:
  • Congruence in Quadrilaterals
  • Congruence Criteria for Polygons
  • Congruence in Space
• Analytical Congruence:
  • Congruence in the Coordinate System
  • Congruence Proof with Vectors
  • Trigonometric Congruence Analysis
• Problem Solving and Proof:
  • Complex Congruence Problems
  • Geometric Proof Techniques
  • Congruence Applications in Space
• Applications:
  • Shape Analysis in Engineering
  • Congruence in Space Designs
  • Trigonometric Modeling
• Affecting Factors:
  • Shape Complexity
  • Use of Coordinates
  • Angle and Side Measurements