Answer:
To prove that KN = NL, we can use the given statements and reasons provided:
1. Given:
N is the midpoint of JL.
N is the midpoint of KM.
JL = KM
2. Definition of Midpoint:
From the given statements, we know that N is the midpoint of both JL and KM. This means that N divides both segments into two equal parts.
3. Segment Addition Postulate:
According to the Segment Addition Postulate, if three points A, B, and C are collinear, then AB + BC = AC. In this case, we can apply the Segment Addition Postulate to segment JL and segment KM:
JL = JN + NL
KM = KN + NM
4. Transitive Property:
Since JL = KM and we can express JL and KM in terms of their components, we can equate the components using the Transitive Property:
JN + NL = KN + NM
5. Simplify:
By rearranging the equation, we have:
JN + NL = KN + NM
JN = KN + NM - NL
JN = KN + (NM - NL)
6. Substitution:
Since N is the midpoint of JL, we know that JN = NL. Substituting this into the equation, we get:
NL = KN + (NM - NL)
7. Simplify:
By simplifying the equation further, we have:
NL - NL = KN + NM - NL
0 = KN + NM - NL
From step 7, we can conclude that KN = NL. This proves that the statement KN = NL is true based on the given information and the logical reasoning used.
Explanation: