prove that every segment is congruent itself
check out the reflexive property of congruence
To prove that every segment is congruent to itself, we need to use the definition of congruence.
In geometry, two segments are said to be congruent if they have the same length.
Now, let's consider a segment AB. To prove that it is congruent to itself, we need to show that the length of AB is equal to the length of AB. This seems obvious, but we should follow a valid geometric proof to demonstrate it formally.
Proof:
1. Consider segment AB.
2. By definition, segment AB is the line segment between points A and B.
3. To find the length of AB, we can use the distance formula or measure it using a ruler.
4. Since the segment is defined by the coordinates of points A and B, the distance between A and B will always be the same for the given segment AB.
5. Therefore, the length of AB is equal to the length of AB.
By following these steps, we have proven that every segment is congruent to itself.