Question

1. n is the midpoint of mp
2. mn = np
3. mn = pr
4. np = pr
5. given

2.

1. given
2. substitution property

use the given information to prove that np = op
given: n is the midpoint of mp,
p is the midpoint of qr,
mn = pr.
prove: np = op

Explanation:

Step1: Mid - point definition

Since \(N\) is the mid - point of \(\overline{MP}\), by the mid - point definition, \(MN = NP\).

Step2: Mid - point definition

Since \(P\) is the mid - point of \(\overline{QR}\), by the mid - point definition, \(QP=PR\).

Step3: Substitution

Given \(MN = PR\), and from Step1 \(MN = NP\), so \(NP = PR\). From Step2 \(QP = PR\), then by substitution \(NP=QP\).

Answer:

1. Mid - point definition.