document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002024>Question 1002024</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can i explain how triangles are similar and how do i solve for missing lengths </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619050 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=619050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Two triangles are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=similar ALIGN=MIDDLE  ALT=\"similar\"   DISABLED_style= \"max-width:90%; height:auto;\" > if they have:\r<BR>\n" );
document.write( "\n" );
document.write( "    all their angles equal<BR>\n" );
document.write( "    corresponding sides are in the same ratio\r<BR>\n" );
document.write( "\n" );
document.write( "But we don't need to know all three sides and all three angles; two or three out of the six is usually enough.\r<BR>\n" );
document.write( "\n" );
document.write( "There are three ways to find if two triangles are similar:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AA ALIGN=MIDDLE  ALT=\"+AA\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SAS ALIGN=MIDDLE  ALT=\"SAS\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SSS ALIGN=MIDDLE  ALT=\"SSS\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AA ALIGN=MIDDLE  ALT=\"AA\"   DISABLED_style= \"max-width:90%; height:auto;\" > stands for \"angle, angle\" and means that the triangles have two of their angles equal (could also be called <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AAA ALIGN=MIDDLE  ALT=\"AAA\"   DISABLED_style= \"max-width:90%; height:auto;\" > because when two angles are equal, all three angles must be equal). \r<BR>\n" );
document.write( "\n" );
document.write( "If two of their angles are equal, then the third angle must also be equal, because angles of a triangle always add to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" >°.\r<BR>\n" );
document.write( "\n" );
document.write( "example: if one angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72 ALIGN=MIDDLE  ALT=\"72\"   DISABLED_style= \"max-width:90%; height:auto;\" >° and second angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" >°, the third<BR>\n" );
document.write( "will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180-%2872+%2B+35%29+=+73 ALIGN=MIDDLE  ALT=\"180-%2872+%2B+35%29+=+73\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SAS ALIGN=MIDDLE  ALT=\"SAS\"   DISABLED_style= \"max-width:90%; height:auto;\" > stands for \"side, angle, side\" and means that we have two triangles where:\r<BR>\n" );
document.write( "\n" );
document.write( "    the ratio between two sides is the same as the ratio between another two sides<BR>\n" );
document.write( "    and we we also know the included angles are equal\r<BR>\n" );
document.write( "\n" );
document.write( "If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.\r<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "\n" );
document.write( "    one pair of sides is in the ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21+%3A+14+=+3+%3A+2 ALIGN=MIDDLE  ALT=\"21+%3A+14+=+3+%3A+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    another pair of sides is in the ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15+%3A+10+=+3+%3A+2 ALIGN=MIDDLE  ALT=\"15+%3A+10+=+3+%3A+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    there is a matching angle of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75 ALIGN=MIDDLE  ALT=\"75\"   DISABLED_style= \"max-width:90%; height:auto;\" >° in between them\r<BR>\n" );
document.write( "\n" );
document.write( "So there is enough information to tell us that the two triangles are similar.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SSS ALIGN=MIDDLE  ALT=\"SSS\"   DISABLED_style= \"max-width:90%; height:auto;\" > stands for \"side, side, side\" and means that we have two triangles with all three pairs of corresponding sides in the same ratio.\r<BR>\n" );
document.write( "\n" );
document.write( "If two triangles have three pairs of sides in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ratio ALIGN=MIDDLE  ALT=\"ratio\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the triangles are similar.\r<BR>\n" );
document.write( "\n" );
document.write( "example:<BR>\n" );
document.write( " the ratios of sides are:\r<BR>\n" );
document.write( "\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3A+x+=+6+%3A+7.5+=+12+%3A+15+=+4+%3A+5 ALIGN=MIDDLE  ALT=\"a+%3A+x+=+6+%3A+7.5+=+12+%3A+15+=+4+%3A+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%3A+y+=+8+%3A+10+=+4+%3A+5 ALIGN=MIDDLE  ALT=\"b+%3A+y+=+8+%3A+10+=+4+%3A+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+%3A+z+=+4+%3A+5 ALIGN=MIDDLE  ALT=\"c+%3A+z+=+4+%3A+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These ratios are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=all ALIGN=MIDDLE  ALT=\"all\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equal ALIGN=MIDDLE  ALT=\"equal\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the two triangles are similar.<BR>\n" );
document.write( "Since the ratios of the lengths of corresponding sides of similar figures are equal, then use this idea to find missing segment lengths in similar figures.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );