## To understand why the two statements are equivalent, it's important to understand the concept of congruence in geometry.

Congruence is a mathematical term that means two geometric figures are identical in shape and size. When we say that "segment AB is congruent to segment CD," we mean that these two line segments have the same length and are identical in shape.

Now, let's break down the two statements:

1. "Segment AB is congruent to segment CD": This statement explicitly states that segment AB and segment CD are congruent, meaning they have the same length and shape.

2. "AB is congruent to CD": This statement uses a shorthand notation to refer to the segments. In geometry, it is common to represent line segments using capital letters with a bar on top of them. So, AB represents segment AB, and CD represents segment CD. By saying "AB is congruent to CD," it is effectively saying that segment AB and segment CD are congruent, just like the first statement.

Therefore, both statements convey the same idea: segment AB is congruent to segment CD. The second statement is simply a more abbreviated way of expressing the congruence of the line segments.