document.write( "Question 177260: Please help with the following question:\r
\n" ); document.write( "\n" ); document.write( "Given: line AB = line AC
\n" ); document.write( "Given: line AD bisects triangle ABC
\n" ); document.write( "Given: point E is in the middle of line AD\r
\n" ); document.write( "\n" ); document.write( "Prove: line BE = line CE
\n" ); document.write( "Prove: triangle AEC = triangle AEB\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "
Algebra.Com's Answer #132361 by gonzo(654)\"\" \"About 
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AB = AC (given)
\n" ); document.write( "AD bisects BC (given)
\n" ); document.write( "BD = DC (bisector of a line splits the line into two congruent parts)
\n" ); document.write( "angle ABC = angle ACB (base angles of isosceles triangle are congruent)
\n" ); document.write( "triangle ABD congruent to triangle ACD (SAS)
\n" ); document.write( "angle ADB = angle ADC (congruent parts of congruent triangles)
\n" ); document.write( "point E is in the middle of line AD (given)
\n" ); document.write( "ED congruent to ED (reflexive property equal to itself)
\n" ); document.write( "triangle BED congruent to triangle CED (SAS)
\n" ); document.write( "BE congruent to EC (congruent parts of congruent triangles)
\n" ); document.write( "AE congruent to AE (reflexive property equal to itself)
\n" ); document.write( "triangle ABE congruent to triangle ACE (SSS)
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