# Congruence and Similarity

## Congruence and Similarity

- “Congruence” and “similarity” are central concepts in geometry.
- Two shapes are congruent if they have the same shape and size. This means they can be placed on top of one another and matched up exactly.
- When two shapes are congruent, all corresponding angles and sides are equal.
- Congruence can be determined using several criteria, including Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Right angle-Hypotenuse-Side (RHS).
- Congruence transformations, or isometrics, include reflections, rotations, and translations. These transformations do not change the size or shape of a figure, hence, the figures before and after transformation are congruent.
- Two shapes are similar if they have the same shape but not necessarily the same size. Basically, one is an enlargement of the other.
- When two shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio.
- Similarity transformations include enlargements and reductions. Unlike congruence transformations, these alter the size of a figure but not its shape, thus, creating similar figures.
- To prove similarity, you can use Angle-Angle (AA), Side-Angle-Side (SAS) or Side-Side-Side (SSS) similarity criteria.
- The ratio of area between two similar shapes equals to the square of the ratio of corresponding sides.
- Understanding congruence and similarity is key for solving many problems in geometry, such as finding missing lengths and angles, or proving that certain figures have specific properties.