Question 176021
Is this what the figure looks like:

<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/geo1.png" border="0" alt="Photobucket">


Note: points N and R are not necessarily the midpoints


Here's a two column proof
<table cellspacing="50">
<th>Statement</th><th>Reason</th>
<tr><td>1. Segment MP = Segment QS</td><td>Given</td></tr>
<tr><td>2. Segment NP = Segment QR</td><td>Given</td></tr>
<tr><td>3. MN + NP = MP</td><td>Segment Addition Postulate</td></tr>
<tr><td>4. QR + RS = QS</td><td>Segment Addition Postulate</td></tr>
<tr><td>5. NP + RS = QS</td><td>Substitution (see statement 2)</td></tr>
<tr><td>6. MN + NP = NP + RS</td><td>Substitution (see statement 1)</td></tr>
<tr><td>7. MN = RS</td><td>Addition Property of Equality</td></tr>
</table>


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.