Astudent solved the following problem and made an error: triangles abc and def. angles a and f are congruent and measure 135 degrees. coordinates for the vertices are at a 0, 2 and b 2, 4 and c 0, 0 and d 2, 0 and e 4, 4 and f 4, 2. line 1 segment ac equals 2. segment fe equals 2. segment ac is congruent to segment fe line 2 ∠a ≅ ∠f line 3 length of segment ab. a (0, 2) b (2, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub 1 squared, d equals square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, d equals square root of negative 2 squared plus negative 2 squared, d equals square root of 4 plus 4, d equals square root of 8 segment ab = 2.83 line 4 length of segment de. d (2, 0) e (4, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub squared, d equals square root of quantity 2 minus 4 all squared plus quantity 0 minus 4 all squared, d equals square root of negative 2 squared plus negative 4 squared, d equals square root of 4 plus 16, then d equals square root of 20 segment de = 4.47 line 5 segment ab is congruent with segment de line 6 triangle abc is congruent with triangle fdeby sas in which line did the student make the first mistake? line 2 line 5 line 3 line 4

We have that
triangle ABC coordinates
A (0,2)  B(2,4)  C(0,0)

triangle DEF coordinates 
D (2,0)  E ( 4,4)  F (4,2)

using a graph tool
see the attached figure

therefore

Line 1 Segment AC equals 2. Segment FE equals 2. Segment AC is congruent to segment FE 
so
Segment AC equals 2-------> is correct
Segment FE equals 2-----> is correct
Segment AC is congruent to segment FE------> is correct

Line 2 ∠A ≅ ∠F------> is correct

Line 3 Length of segment AB. A (0, 2) B (2, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub 1 squared, d equals square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, d equals square root of negative 2 squared plus negative 2 squared, d equals square root of 4 plus 4, d equals square root of 8 segment AB = 2.83

find the distance AB
d=√[(4-2)²+(2-0)²]--------> d=√[4+4]-----> d=√8-----> d=2.83
AB=2.83
so
Line 3 is correct

Line 4 Length of segment DE. D (2, 0) E (4, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub squared, d equals square root of quantity 2 minus 4 all squared plus quantity 0 minus 4 all squared, d equals square root of negative 2 squared plus negative 4 squared, d equals square root of 4 plus 16, then d equals square root of 20 segment DE = 4.47

find the distance DE
d=√[(4-0)²+(4-2)²]--------> d=√[16+4]-----> d=√20-----> d=4.47
DE=4.47
so
Line 4------> is correct

Line 5 segment AB is congruent with segment DE
AB is not congruent with DE
so
Line 5 is not correct

therefore

the answer is
the student make the first mistake in line 5

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