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.