document.write( "Question 1013605: given: parallelogram ABCD, line DE is perpendicular to line AC, line BF is perpendicular to line AC
\n" ); document.write( "prove: triangle ADE is congruent to triangle CBF
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #630022 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "given: parallelogram ABCD, line DE is perpendicular to line AC, line BF is perpendicular to line AC
\n" ); document.write( "prove: triangle ADE is congruent to triangle CBF
\n" ); document.write( "----------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "0. Make a sketch. It is intended not to replace the proof, but to help you follow the proof.\r\n" );
document.write( "\r\n" );
document.write( "1. Consider these two triangles, ADE and CFB.\r\n" );
document.write( "   Notice that these triangles are right-angled triangles.\r\n" );
document.write( "\r\n" );
document.write( "2. Their sides AD and BC are congruent as the opposite sides of the parallelogram.\r\n" );
document.write( "\r\n" );
document.write( "3. These triangles have congruent angles LDAE and LFCB, since these angles are alternate interior angles \r\n" );
document.write( "   at the parallel lines AD and BA and the transverse AC.\r\n" );
document.write( "\r\n" );
document.write( "4. Since the right angled triangles ADE and CFB have the pair of congruent acute angles LDAE and LFCB, \r\n" );
document.write( "   they have the other pair of acute angles LADE and LCBF congruent too.\r\n" );
document.write( "\r\n" );
document.write( "5. Now the triangles ADE and CFB are congruent according to the ASA-test of congruency of triangles.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Regarding parallel line, see the lesson Parallel lines in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Regarding tests on congruency of triangles, see the lesson Congruence tests for triangles.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );