document.write( "Question 966259: Given: Quad ABCD is a trapezoid
\n" ); document.write( "Prove: A(Triangle ACD) = A(Triangle BCD)\r
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Algebra.Com's Answer #590557 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "Let  ABCD  be a trapezoid with the bases  AB  and  DC,  and  AC  and  BD  be its diagonals.                       \r
\n" ); document.write( "\n" ); document.write( "(Figure 1).  We need to prove that the triangles  \"DELTA\"ACD  and  \"DELTA\"BCD  have equal areas. \r
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\n" ); document.write( "\n" ); document.write( "Let us draw the altitudes  AE  and  BF  in the trapezoid  ABCD  from vertices  A  and  B  \r
\n" ); document.write( "\n" ); document.write( "to the base  DC  (Figure 1). \r
\n" ); document.write( "\n" ); document.write( "Notice that these altitudes are congruent as the opposite sides of the rectangular  ABFE. \r
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\n" ); document.write( "\n" ); document.write( "Now,  the triangles  \"DELTA\"ACD  and  \"DELTA\"BCD  share the common base  DC  and have \r
\n" ); document.write( "\n" ); document.write( "congruent altitudes to the base.  Therefore,  these triangles have the same area.\r
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