Question

1. transitive property of segment congruence

given ▸ $overline{ab}congoverline{jk},overline{jk}congoverline{st}$
prove ▸ $overline{ab}congoverline{st}$

statements	reasons
2. $ab = jk,jk = st$	2. ?
3. $ab = st$	3. ?
4. $overline{ab}congoverline{st}$	4. ?

Explanation:

Step1: Given information

Given

Step2: Definition of congruent segments

If two segments are congruent, their lengths are equal.

Step3: Transitive property of equality

If \(a = b\) and \(b = c\), then \(a = c\). Here \(a = AB\), \(b = JK\), \(c = ST\).

Step4: Definition of congruent segments (reverse - from equal lengths to congruence)

If the lengths of two segments are equal, the segments are congruent.

Answer:

1. Given
2. Definition of congruent segments
3. Transitive property of equality
4. Definition of congruent segments