Question

complete the two - column proof for the reflexive property of segment congruence (thm. 2.1). statements 1. a segment exists with endpoints a and b. 2. 3. 4. $overline{ab}congoverline{ab}$

Explanation:

Step1: State the definition of congruence

Congruent segments have equal lengths.

Step2: Note the length of a segment

The length of $\overline{AB}$ is $AB$. And $AB = AB$ by the reflexive property of equality.

Step3: Connect length - equality to segment - congruence

Since the lengths of $\overline{AB}$ and $\overline{AB}$ are equal (i.e., $AB = AB$), by the definition of congruent segments (segments with equal lengths are congruent), we have $\overline{AB}\cong\overline{AB}$.

Answer:

1. The length of $\overline{AB}$ is $AB$.
2. $AB = AB$ (by the reflexive property of equality).