document.write( "Question 54898This question is from textbook Roads to Geometry
\n" ); document.write( ": The problem is: The area of a rhombus is one-half the product of the lengths of its diagonals.\r
\n" ); document.write( "\n" ); document.write( "I know the answer as with the previous problem, I just do not know how to go about writing a proof for this.\r
\n" ); document.write( "\n" ); document.write( "Thank You \n" ); document.write( "
Algebra.Com's Answer #37076 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
The problem is: The area of a rhombus is one-half the product of \r\n" );
document.write( "the lengths of its diagonals. \r\n" );
document.write( "I know the answer as with the previous problem, I just do not know \r\n" );
document.write( "how to go about writing a proof for this. \r\n" );
document.write( "Thank You\r\n" );
document.write( "\r\n" );
document.write( "I won't do it in numbered steps and reasons.  You can do that. I'll \r\n" );
document.write( "just explain what you do to prove it.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    A                     Given: Rhombus ABCD\r\n" );
document.write( "   /|\                    To prove: Area of Rhombus ABCD = DB×AC/2\r\n" );
document.write( "  / | \\r\n" );
document.write( "D/ E|  \B\r\n" );
document.write( " \¯¯|¯¯/\r\n" );
document.write( "  \ | /\r\n" );
document.write( "   \|/ \r\n" );
document.write( "   C\r\n" );
document.write( "\r\n" );
document.write( "Area of rhombus ABCD = area of triangle ABD + area of \r\n" );
document.write( "triangle CBD\r\n" );
document.write( "\r\n" );
document.write( "Triangles ABD and CBD are congruent by SSS\r\n" );
document.write( "\r\n" );
document.write( "Area of rhombus ABCD = 2×(Area of triangle ABD)\r\n" );
document.write( "\r\n" );
document.write( "AE is perpendicular to DB because the diagonals \r\n" );
document.write( "of a rhombus are perpendicular bisectors of each other.\r\n" );
document.write( "\r\n" );
document.write( "Area of triangle ABD = DB×AE/2 because a triangle's area\r\n" );
document.write( "is one-half the product of a side and the altitude drawn\r\n" );
document.write( "to that side.\r\n" );
document.write( "\r\n" );
document.write( "Area of rhombus ABCD = 2×(Area of triangle ABD)\r\n" );
document.write( "\r\n" );
document.write( "So area of rhombus ABCD = 2×(DB×AE/2) = DB×AE\r\n" );
document.write( "\r\n" );
document.write( "AE = AC/2 because the diagonals of a rhombus are perpendicular\r\n" );
document.write( "bisectors of each other.\r\n" );
document.write( "\r\n" );
document.write( "So area of rhombus DB×AE = DB×(AC/2) = DB×AC/2\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );