Side-Side-Side (SSS) (Postulate 12) If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) (Postulate 13)
If two sides and the included angle of a second triangle, then the two triangles are congruent.
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then two triangles are congruent.
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
NO - Angle-Side-Side (ASS)
The "ASS" postulate does not work, unlike the other ones. A way that students can remember this is that "ass" is not a nice word, so we don't use it in geometry (since it does not work).
- 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:
- Two and Three-Dimensional Geometry and Other Geometric Figures
- Geometry/Perimeter and Arclength
- Geometry/Right Triangles and Pythagorean Theorem
- 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/Ellipsoids and Spheres
- Geometry/Coordinate Systems (currently incorrectly linked to Astronomy)
- Traditional Geometry:
- Modern geometry