SOLUTION: hi tutor! may you please help me with this complicated question. I already saw an answer posted to someone else's same question, but i dont think its right. can someone else help m

Question 176021This question is from textbook Geometry
: hi tutor! may you please help me with this complicated question. I already saw an answer posted to someone else's same question, but i dont think its right. can someone else help me pease with this one, i would rather have a different answer than the other one please.Thanks for the effort. i appreciate all your help.
Given: segment MP is congruent to segment QS. Segment NP is congruent to segment QR.
Prove: Segment MN is conruent to segment RS.
M is on the top left, P is on the top right, Q is on the bottom left, S is on the bottom right, N is between M and P while R is between Q and S.Thanks again.This question is from textbook Geometry

Answer by jim_thompson5910(21685) (Show Source):
You can put this solution on YOUR website!
Is this what the figure looks like:

Note: points N and R are not necessarily the midpoints

Here's a two column proof

Statement Reason
1. Segment MP = Segment QS Given

2. Segment NP = Segment QR Given

3. MN + NP = MP Segment Addition Postulate

4. QR + RS = QS Segment Addition Postulate

5. NP + RS = QS Substitution (see statement 2)

6. MN + NP = NP + RS Substitution (see statement 1)

7. MN = RS Addition Property of Equality

Note: In statement 1, it is given that MP = QS. Since MP = MN + NP and QS = NP + RS, I did a substitution and plugged in these expressions into MP = QS to get MN + NP = NP + RS.