Question

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

Answer 1

The first statement is Given, the second is the Definition of a Midpoint, and the third is Definition of Congruence, so it is C.

Answer 2

Option: c is correct.

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

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)