Intermediate Geometry explores the properties and relationships of shapes, sizes, and theorems in two and three dimensions.
Two shapes are congruent if they are exactly the same in size and shape, even if flipped or rotated. Similar shapes have the same shape but not necessarily the same size — they are proportional.
Congruence is used in manufacturing identical parts. Similarity helps when creating models or scaling images up or down.
Imagine two triangles: one is a larger version of the other with all angles the same. They are similar, not congruent!
\[\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\]
Blueprints use similar shapes to represent buildings at a smaller scale.
Puzzle pieces must be congruent to fit together perfectly.
Similarity is about proportional shapes; congruence is about being identical in every way.