document.write( "Question 1093258: Given: A (2,3), B (5,-1), C (1,0), D (-4,-1), E(O,2), F(-1,-2)
\n" ); document.write( "Prove: Triangle ABC is congruent to triangle DEF
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Algebra.Com's Answer #707883 by greenestamps(13206) $\"\"$ $\"About$

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Use the distance formula to show that AB=DE, AC=DF, and BC=EF.

\n" ); document.write( "Note that, with integer inputs, the distance formula often (usually) gives answers involving square roots. But if two lengths involving square roots are equal, then the squares of those lengths are also equal. So in using the distance formula, we don't need to deal with the square roots at all.

\n" ); document.write( "So to show AB=DE, we have
\n" ); document.write( " $\"%285-2%29%5E2+%2B+%283-%28-1%29%29%5E2+=+3%5E2%2B4%5E2+=+25\"$ for the square of the length of AB, and
\n" ); document.write( " $\"%28-4-0%29%5E2+%2B+%282-%28-1%29%29%5E2+=+4%5E2%2B3%5E2+=+25\"$ for the square of the length of DE.

\n" ); document.write( "So legs AB and DE are the same length.

\n" ); document.write( "Perform the similar calculations to show the other pairs of corresponding sides are the same lengths. \n" ); document.write( "

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