## Methods of Determining CongruenceEdit

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 ProofsEdit

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

- 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