Question

2 given: $overline{kl}congoverline{ln}$, $overline{lm}congoverline{ln}$ prove: $l$ is the mid - point of $overline{km}$ statements reasons 1. $overline{kl}congoverline{ln}$, $overline{lm}congoverline{ln}$ 1. 2. $kl = ln$, $lm = ln$ 2. 3. $kl = lm$ 3. 4. $l$ is the mid - point of $overline{km}$ 4. 3 given: $overline{pq}congoverline{tq}$, $overline{uq}congoverline{qs}$ prove: $overline{ps}congoverline{tu}$

Explanation:

Step1: Given

1. $\overline{KL}\cong\overline{LN},\overline{LM}\cong\overline{LN}$ (Given)

Step2: Definition of congruent segments

1. $KL = LN, LM=LN$ (If two segments are congruent, their lengths are equal)

Step3: Transitive property of equality

1. $KL = LM$ (Since $KL = LN$ and $LM = LN$, by transitive property)

Step4: Definition of mid - point

1. $L$ is the midpoint of $\overline{KM}$ (A point that divides a segment into two equal - length segments is the midpoint)

Answer:

Statements	Reasons
2. $KL = LN, LM = LN$	2. Definition of congruent segments
3. $KL = LM$	3. Transitive property of equality
4. $L$ is the midpoint of $\overline{KM}$	4. Definition of mid - point