# Geometry/Congruency and Similarity

## Congruency[edit]

*Congruent* shapes are the same size with corresponding lengths and angles equal. In other words, they are exactly the same size and shape. They will fit on top of each other perfectly. Therefore if you know the size and shape of one you know the size and shape of the others. For example:

Each of the above shapes is congruent to each other. The only difference is in their orientation, or the way they are rotated. If you traced them onto paper and cut them out, you could see that they fit over each other exactly.

Having done this, right away we can see that, though the angles correspond in size and position, the sides do not. Therefore it is proved the triangles are **not** congruent.

## Similarity[edit]

*Similar* shapes are like congruent shapes in that they must be the same shape, but they don't have to be the same size. Their corresponding angles are congruent and their corresponding sides are in proportion.

- 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:

- 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:

- Modern geometry