Describe the difference between saying that two segments are congruent and saying that two segments have equal length. When would you use each phrase?
conguent refers to two objects
length describes properties of the objects
two polygons are congruent if all their sides and angles have equal measure. Saying two objects are congruent is a short way of saying that all their properties are the same. Saves a lot of time.
When we say that two segments are congruent, it means that they are identical in length, shape, and orientation. In other words, they are exactly the same. On the other hand, when we say that two segments have equal length, it implies that the lengths of the two segments are the same, but their shapes and orientations may be different.
To determine whether two segments are congruent, we need to use congruence criteria, such as the Side-Side-Side, Side-Angle-Side, or Angle-Side-Angle criteria, depending on the specific situation. These criteria involve comparing the lengths and angles of the given segments.
On the other hand, to determine whether two segments have equal length, we can simply measure the lengths of the two segments using a ruler or any measuring device. This empirical method does not require any geometric reasoning or congruence criteria.
So, in summary, we use the phrase "congruent segments" when we want to emphasize that two segments are exactly the same in terms of length, shape, and orientation, and we rely on congruence criteria to establish this. On the other hand, we use the phrase "segments with equal length" when we are referring to two segments whose lengths are the same, but their shapes and orientations may differ. In this case, we can measure the lengths to determine their equality.