Question

proof complete the flow proof to prove that if point m is the mid - point of $overline{ln}$, point l is the mid - point of $overline{ab}$ and $al = mn$, then $lm = lb$. drag the statements and reasons to complete the proof.
m is the midpoint of $overline{ln}$
l is the midpoint of $overline{ab}$
$al = mn$
$overline{lm}congoverline{mn}$
midpoint theorem
midpoint theorem
$al = lb$
$lm = lb$
def. of congruent segments
substitution
transitive prop. of equality
def. of congruent segments $lm = al$ $overline{al}congoverline{lb}$
given $lm = mn$
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Explanation:

Step1: Use mid - point property for $LN$

Since $M$ is the mid - point of $\overline{LN}$, by the mid - point theorem, $LM = MN$.

Step2: Use mid - point property for $AB$

Since $L$ is the mid - point of $\overline{AB}$, by the mid - point theorem, $AL = LB$.

Step3: Substitute equal segments

Given $AL = MN$, and since $LM = MN$ and $AL = LB$, by the transitive property of equality, $LM = LB$.

Answer:

Drag "LM = MN" to the first blank under "M is the mid - point of LN, L is the mid - point of AB, AL = MN" using the mid - point theorem. Drag "AL = LB" to the second blank under the same using the mid - point theorem. Drag "LM = AL" to the first blank under "Def. of congruent segments" (because if $LM = MN$ and $AL = MN$, then $LM = AL$). Drag "$\overline{AL}\cong\overline{LB}$" to the blank under "Midpoint Theorem" for the $AB$ segment.