<p>points Q,R, and S lie on line l in that order, and point P is not on l. If PQ = PS, which of the following must be true
PQ > PR, PQ > QR, PQ > QS, PR > RS, QR > RS</p>
<p>I'm trying to understand why it's PQ > PR ... apart from just "seeing it"</p>
<p>is it because the line QR would have to be at the same angle as PQ if it were equal?</p>
<p>I just see it as…:
…(P)
…(P)
Q-----R-----S
…(P)
…(P)</p>
<pre><code> Now PQ > PR because if you think of a triangle QRP, PQ would be the hypotenuse, or the greatest side.
</code></pre>
<p>First draw a picture. Then use the following fact: “Sides opposite bigger angles are longer.”</p>
<p>Remark: You may want to draw 3 pictures to see all the cases: one where R is “in the middle,” one where R is close to Q, and one whee R is close to S.</p>
<p>By the way, can you tell me what test this problem came from?</p>
<p>thanks. and 5/09</p>