document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209159>Question 1209159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the diagram, ABCG is a parallelogram, and BF = 18 cm, FE = 6 cm. Find the length, in cm, of ED.<BR>\n" );
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document.write( "Angles AEF and CBF are congruent (parallel lines cut by a transversal).<BR>\n" );
document.write( "Likewise angles EAF and BCF are congruent.<br><BR>\n" );
document.write( "So triangles AEF and CBF are similar; and legs EF and BF, for which lengths are given, are corresponding parts of those similar triangles.<br><BR>\n" );
document.write( "Since those lengths are 18 and 6, the ratio of similarity between the two triangles is 3:1.<br><BR>\n" );
document.write( "That means BC is 3 times the length of AE; and that means EG is twice the length of AE.<br><BR>\n" );
document.write( "Angles BAG and AGC are supplementary (adjacent angles in parallelogram ABCG), so angles AGD and BAE are congruent.<br><BR>\n" );
document.write( "That makes triangles BAE and DGE similar; and with EG twice AE, the ratio of similarity between those two triangles is 2:1.<br><BR>\n" );
document.write( "And BE, with length 18+6=24, and ED are corresponding parts of those two triangles, so the length of ED is twice the length of BE, or 2*24 = 48.<br><BR>\n" );
document.write( "ANSWER: 48<br><BR>\n" );
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