Figures that have the same shape and size are known as congruent figures. In geometry, two shapes are considered congruent if they can be perfectly overlaid on top of each other through a series of rigid transformations, which include translations (sliding), rotations (turning), and reflections (flipping). This implies that both the dimensions and form of the figures are identical.
For example, if you have two triangles that have the same length for each corresponding side and the same measure for each corresponding angle, then you can say that these triangles are congruent. The notation used to denote congruent figures is typically represented by the symbol ∼, indicating that these two shapes are congruent to each other.
Congruence is a foundational concept in geometry and is utilized in various applications, from solving mathematical problems to ensuring that designs and constructions are accurate. Understanding congruence helps in visualizing and validating the properties of shapes in both theoretical and practical contexts.