Geometry/Congruent Triangles

Methods of Determining Congruence

Two triangles are congruent if:

• each pair of corresponding sides is congruent
• two pairs of corresponding angles are congruent and a pair of corresponding sides are congruent
• two pairs of corresponding sides and the angles included between them are congruent

Tips for Proofs

Commonly used prerequisite knowledge in determining the congruence of two triangles includes:

• by the reflexive property, a segment is congruent to itself
• vertical angles are congruent
• when parallel lines are cut by a transversal corresponding angles are congruent
• when parallel lines are cut by a transversal alternate interior angles are congruent
• midpoints and bisectors divide segments and angles into two congruent parts

Navigation

• Geometry
• Part I- Euclidean Geometry:
  • Chapter 1. Geometry/Points, Lines, Line Segments and Rays
  • Chapter 2. Geometry/Angles
  • Chapter 3. Geometry/Properties
  • Chapter 4. Geometry/Inductive and Deductive Reasoning
  • Chapter 5. Geometry/Proof
  • Chapter 6. Geometry/Five Postulates of Euclidean Geometry
  • Chapter 7. Geometry/Vertical Angles
  • Chapter 8. Geometry/Parallel and Perpendicular Lines and Planes
  • Chapter 9. Geometry/Congruency and Similarity
  • Chapter 10. Geometry/Congruent Triangles
  • Chapter 11. Geometry/Similar Triangles
  • Chapter 12. Geometry/Quadrilaterals
  • Chapter 13. Geometry/Parallelograms
  • Chapter 14. Geometry/Trapezoids
  • Chapter 15. Geometry/Circles/Radii, Chords and Diameters
  • Chapter 16. Geometry/Circles/Arcs
  • Chapter 17. Geometry/Circles/Tangents and Secants
  • Chapter 18. Geometry/Circles/Sectors
  • Appendix A. Geometry/Postulates & Definitions
  • Appendix B. Geometry/The SMSG Postulates for Euclidean Geometry

• Part II- Coordinate Geometry:
  • Geometry/Synthetic versus analytic geometry

• Two and Three-Dimensional Geometry and Other Geometric Figures
  • Geometry/Perimeter and Arclength
  • Geometry/Area
  • Geometry/Volume
  • Geometry/Polygons
  • Geometry/Triangles
  • Geometry/Right Triangles and Pythagorean Theorem
  • Geometry/Polyominoes
  • Geometry/Ellipses
  • Geometry/2-Dimensional Functions
  • Geometry/3-Dimensional Functions
  • Geometry/Area Shapes Extended into 3rd Dimension
  • Geometry/Area Shapes Extended into 3rd Dimension Linearly to a Line or Point
  • Geometry/Polyhedras
  • Geometry/Ellipsoids and Spheres
  • Geometry/Coordinate Systems (currently incorrectly linked to Astronomy)

• Traditional Geometry:
  • Geometry/Topology
  • Geometry/Erlanger Program
  • Geometry/Hyperbolic and Elliptic Geometry
  • Geometry/Affine Geometry
  • Geometry/Projective Geometry
  • Geometry/Neutral Geometry
  • Geometry/Inversive Geometry

• Modern geometry
  • Geometry/Algebraic Geometry
  • Geometry/Differential Geometry
  • Geometry/Algebraic Topology
  • Geometry/Noncommutative Geometry

• Geometry/An Alternative Way and Alternative Geometric Means of Calculating the Area of a Circle