Question

proof complete the flow - proof to prove that if point m is the midpoint of ln, point l is the midpoint of ab, and al = mn, then lm = lb. drag the statements and reasons to complete the proof. substitution def. of congruent segments midpoint theorem lm ≅ mn m is the midpoint of ln l is the midpoint of ab al = mn transitive prop. of equality lm = lb al = lb midpoint theorem

Explanation:

Step1: Recall mid - point theorem

If \(L\) is the mid - point of \(\overline{AB}\), by the mid - point theorem, \(AL = LB\).

Step2: Use given equality

Given \(AL = MN\).

Step3: Use transitive property

Since \(AL = LB\) and \(AL = MN\), by the transitive property of equality, if \(a=b\) and \(a = c\), then \(b = c\). So \(LB=MN\).

Step4: Use mid - point theorem and congruence

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

Step5: Substitute

Substitute \(MN\) with \(LB\) (from step 3) into \(LM = MN\). We get \(LM = LB\).

Answer:

The proof is completed by using the mid - point theorem, given equalities, and the transitive property of equality to show that \(LM = LB\).