document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763743>Question 763743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete each statement with the word always, sometimes, or never.<BR>\n" );
document.write( "In a plane, two lines perpendicular to the same line are _______ parallel.<BR>\n" );
document.write( "If two lines are a cut by a transversal, corresponding angles are _____ congruent.<BR>\n" );
document.write( "A transversal perpendicular to one of two parallel lines is _____ perpendicular to the other line. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464987 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=464987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "In a plane, two lines perpendicular to the same line are _______ parallel.\r<BR>\n" );
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document.write( "Two lines are perpendicular to the same line. So this means that the two <BR>\n" );
document.write( "form a set of right angles. This further tells us that the same side <BR>\n" );
document.write( "interior angles are supplementary, and by the converse of the same side <BR>\n" );
document.write( "interior angles theorem, the two lines are parallel. So this is <font color=\"red\">always true</font>\r<BR>\n" );
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document.write( "Note: this is of course assuming the two lines are distinct\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "If two lines are a cut by a transversal, corresponding angles are _____ congruent.\r<BR>\n" );
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document.write( "This is only true if the two lines (excluding the transversal) are parallel. <BR>\n" );
document.write( "So this is <font color=\"red\">sometimes true</font>.\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "A transversal perpendicular to one of two parallel lines is _____ perpendicular to the other line.\r<BR>\n" );
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document.write( "Let's make lines m and n parallel, so m || n. Now let's make line k <BR>\n" );
document.write( "perpendicular to line m.\r<BR>\n" );
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document.write( "If line k is perpendicular to line m, then we have a right angle in the <BR>\n" );
document.write( "interior where k and m intersect. So by the same side interior angles <BR>\n" );
document.write( "theorem, the two same side interior angles are supplementary, which means <BR>\n" );
document.write( "the other interior angle on the other side must be 90 degrees as well (since <BR>\n" );
document.write( "90+x=180 leads to x = 90). This proves that lines k and n intersect at right <BR>\n" );
document.write( "angles as well\r<BR>\n" );
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document.write( "So this is <font color=\"red\">always true</font>\r<BR>\n" );
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document.write( "Complete each statement with the word always, sometimes, or never.\r<BR>\n" );
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document.write( "In a plane, two lines perpendicular to the same line are ___<u><font color=\"red\">always</font></u>____ parallel.<BR>\n" );
document.write( "If two lines are a cut by a transversal, corresponding angles are __<u><font color=\"red\">sometimes</font></u>___ congruent (it's only true if the two lines are parallel)<BR>\n" );
document.write( "A transversal perpendicular to one of two parallel lines is __<u><font color=\"red\">always</font></u>___ perpendicular to the other line. </SPAN>\n" );
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