What term describes shapes that are identical in both shape and size?

The term that describes shapes that are identical in both shape and size is "congruent." When two shapes are congruent, they can be superimposed on each other perfectly, meaning every corresponding side and angle is equal. This concept is fundamental in geometry, particularly in the study of triangles and other polygons, where proving congruence can be a key part of solving problems related to these shapes.

Other terms, such as "similar," refer to shapes that may have the same shape but differ in size. "Equilateral" specifically refers to triangles where all three sides are of equal length, which does not encompass all congruent shapes. "Parallel" describes lines that run alongside each other at equal distances apart and never intersect, which isn't related to the concept of congruence in shapes. Thus, congruence is the accurate descriptor for shapes that are exactly the same in both dimensions and angles.