Question

activity 1: whats the segment? prove the conjecture: if ab is a segment in the plane and cd is a segment in the plane with the same length as ab, then ab is congruent to cd.

Explanation:

Step1: Recall the definition of congruent segments

Two segments are congruent if and only if they have the same length.

Step2: Apply the given information

We are given that segment \(AB\) and segment \(CD\) have the same length. By the definition of congruent - segments, if two segments have the same length, they are congruent. So, \(AB\cong CD\).

Answer:

The conjecture is proven since by the definition of congruent segments (two segments are congruent if and only if they have the same length), and given that \(AB\) and \(CD\) have the same length, \(AB\) is congruent to \(CD\).