Answer: 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.
