Fill in the missing reasons for the following two-column proof for the following information.

given: m is the midpoint of pq; mq = 12
prove: pm = 12

a) 1. given; 2. definition of congruence; 3. definition of midpoint
b) 1. given; 2. definition of congruence; 3. substitution
c) 1. given; 2. definition of midpoint; 3. definition of congruence
d) 1. given; definition of midpoint; 3. substitution

Option: c is correct.

d) 1. Given; Definition of Midpoint; 3. Definition of congruence.

Step-by-step explanation:

We are given that M is the midpoint of PQ such that:

MQ=12

Now we are asked to prove:

PM=12

      Statement                                           Reason

M is the mid-point of PQ; MQ=12              Given

    PM=MQ                                                  definition of mid-point

PM=12                                                        definition of

                                                                      congruence.  

( As we know that a mid-point divide the line segment into two equal parts, Hence, the length of the two parts will be equal.

Hence, Reason 2 is a definition of a mid-point)