Geometry/Properties

Triangle Properties

Triangle congruency.

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.

'Angle-Side-Angle' (ASA)

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.

'Angle-Angle-Side' (AAS)

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).

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