What would you use to describe two shapes that perfectly overlap when placed on top of each other?

When two shapes perfectly overlap when placed on top of each other, they are described as congruent. This means that they have the same size and shape, which allows for perfect alignment without any gaps or discrepancies.

Congruent shapes will have identical corresponding angles and side lengths, ensuring that every part matches exactly with the other shape. This concept is essential in geometry as it allows for the comparison and analysis of shapes based on their physical characteristics, providing insight into their properties and relationships.

The other terms mentioned, such as similar, equivalent, and complementary, refer to different relationships between shapes. Similar shapes have the same shape but not necessarily the same size; they are proportional but not congruent. Equivalent often refers to quantities or measures that are equal in value rather than in physical dimensions. Complementary usually describes angles that add up to a right angle and does not pertain to the overlap of shapes. Hence, the concept of congruence accurately captures the idea of identical overlapping shapes.