document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192149>Question 1192149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Let  be five points, no three of which are collinear. How many lines contain two of these five points?\r<BR>\n" );
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document.write( "2.If no four of the five points are coplanar, how many planes contain three of the five points?\r<BR>\n" );
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document.write( "Hint: (for 1 and 2, list all the lines and the planes as sets)\r<BR>\n" );
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document.write( "3.Suppose you have n points, no three of which are collinear. How many lines contain two of these n points?\r<BR>\n" );
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document.write( "4.If no four of the n points are coplanar, how many planes contain three of the n points?<BR>\n" );
document.write( "Hint: (for 3 and 4, generalize in a form of a formula)\r<BR>\n" );
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document.write( "5.Prove theorem 1.1.4. The steps in the proof are already given: you just have to supply the reasons for each step.\r<BR>\n" );
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document.write( "Theorem 1.1.4. If two lines intersect, then their union lies in exactly one plane.\r<BR>\n" );
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document.write( "Proof: Let  and  be two intersecting lines.<BR>\n" );
document.write( " ∩  is a point p.<BR>\n" );
document.write( " contains a point q ≠ p.<BR>\n" );
document.write( "There is a plane E, containing  and q.<BR>\n" );
document.write( "E contains  ∪ .<BR>\n" );
document.write( "No other plane contains  ∪ . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824197 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Just was answered and solved under this link\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Geometry-proofs/Geometry_proofs.faq.question.1192278.html\r<BR>\n" );
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document.write( "If you want to get benefits from this forum, then ask one question/problem per post.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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