document.write( "Question 1174792: Question: Which Of The Following Uses The Given Set Of Points To Prove That ABC A EFD? A(0,0), B (3.0), C(2,3), D(3.0), E (1,3), F (4,3) AB = EF = 761, BC = FD = 34, CA = DE = 5, And ABC AEFD By SAS. AB = EF = V13, BC = FD = V10, CA = DE = 3, And A ABC AEFD By SSS. AB = EF = 9, BC = FD = 10, CA = DE = 13, And ABC > EFD By SAS « \n" ); document.write( "
Algebra.Com's Answer #850633 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
Let's calculate the side lengths of triangles ABC and EFD to determine which congruence criterion applies.\r
\n" ); document.write( "\n" ); document.write( "**Triangle ABC:**\r
\n" ); document.write( "\n" ); document.write( "* AB = √((3 - 0)² + (0 - 0)²) = √(3² + 0²) = √9 = 3
\n" ); document.write( "* BC = √((2 - 3)² + (3 - 0)²) = √((-1)² + 3²) = √(1 + 9) = √10
\n" ); document.write( "* CA = √((0 - 2)² + (0 - 3)²) = √((-2)² + (-3)²) = √(4 + 9) = √13\r
\n" ); document.write( "\n" ); document.write( "**Triangle EFD:**\r
\n" ); document.write( "\n" ); document.write( "* EF = √((4 - 1)² + (3 - 3)²) = √(3² + 0²) = √9 = 3
\n" ); document.write( "* FD = √((3 - 4)² + (0 - 3)²) = √((-1)² + (-3)²) = √(1 + 9) = √10
\n" ); document.write( "* DE = √((1 - 3)² + (3 - 0)²) = √((-2)² + 3²) = √(4 + 9) = √13\r
\n" ); document.write( "\n" ); document.write( "**Comparison:**\r
\n" ); document.write( "\n" ); document.write( "* AB = EF = 3
\n" ); document.write( "* BC = FD = √10
\n" ); document.write( "* CA = DE = √13\r
\n" ); document.write( "\n" ); document.write( "Since all three sides of triangle ABC are congruent to the corresponding sides of triangle EFD, we can conclude that the triangles are congruent by the Side-Side-Side (SSS) criterion.\r
\n" ); document.write( "\n" ); document.write( "Therefore, the correct statement is:\r
\n" ); document.write( "\n" ); document.write( "* AB = EF = 3, BC = FD = √10, CA = DE = √13, and ∆ABC ≅ ∆EFD by SSS.
\n" ); document.write( " \n" ); document.write( "
\n" );