Simply put the term corresponding in math refers to objects such as angles which appear in the same exact place, in two similar situations.

Sides and angles can be considered as corresponding when a pair of matching angles or sides are in the same position in two different shapes.

Corresponding Corresponding objects are those that appear in the same place in two similar situations. It often happens with angles as shown below.

Corresponding sides are the pair of matching sides that are placed at the same spot in two different shapes. Corresponding sides and corresponding angles are compared to study similarity and congruence. Corresponding parts are the parts that appear in identical places in two similar shapes.

A correspondence between two sets $ A $ and $ B $ is any subset $ R $ of the Cartesian product $ A times B $. In other words, a correspondence between $ A $ and $ B $ consists of certain ordered pairs $ (a, b) $, where $ a in A $ and $ b in B $.