Aconjecture and the two-column proof used to prove the conjecture are shown.

the statements and resons, from the given bench, that fill in the blank are shown in italic and bold in this table:

    Statement                                                        Reason

1. K is the midpoint of segment JL                      Given

2. segment JK ≅ segment KL                             Definition of midpoint

3. L is the midpoint of segment KM                 Given

4. segment KL ≅ segment LM                           Definition of midpoint

5. segment JK ≅ segment LM                           Transitive Property of

                                                                             Congruence

Explanation:

1. First blank: you must indicate the reason of the statement "segment JK ≅ segment KL". Since you it is given that K is the midpoint of segment JL,  the statement follows from the very Definition of midpoint.

2. Second blank: you must add a given statement. The other given statement is segment KL ≅ segment LM .

3. Third blank: you must indicate the statement that corresponds to the definition of midpoint. That is segment KL ≅ segment LM .

4. Fourth and fith blanks: you must indicate the statement and reason necessary to conclude with the proof. Since, you have already proved that segment JK ≅ segment KL and segment KL ≅ segment LM it is by the transitive property of congruence that  segment JK ≅ segment LM.

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