A student solved the following problem and made an error:

Triangles ABC and DEF. Angles A and F are congruent and measure 135 degrees. The 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 DF equals 2, segment AC is congruent to segment DF
Line 2 ∠A ≅ ∠F
Line 3 Length of segment AB.
A (0, 2)
B (2, 4)
d equals square root of quantity x sub 1 minus x sub 2 squared plus quantity y sub 1 minus y sub 2 squared, then d equals the square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, then d equals the square root of negative 2 squared plus negative 2 squared, then d equals the square root of 4 plus 4, then d equals the square root of 8
segment AB = 2.83
Line 4 Length of segment FD.
D (2, 0)
F (4, 2)
d equals the square root of quantity x sub 1 minus x sub 2 squared plus quantity y sub 1 minus y sub 2 squared then d equals the square root of quantity 2 minus 4 all squared plus quantity 0 minus 2 all squared, then d equals the square root of negative 2 squared plus negative 2 squared, then d equals the square root of 4 plus 4, then d equals the square root of 8
segment FD = 2.83
Line 5 segment AC is congruent to segment FD
Line 6 triangle ABC is congruent to triangle FDE by SAS

In which line did the student make the first mistake?

Triangle ABC is congruent to triangle FDE by SAS congruence. Therefore, students did mistake in line 1.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, in triangles ABC and DEF

∠A≅∠F=135°

The coordinates for the vertices are at A(0, 2), B(2, 4) and C(0, 0)

In triangle DEF, we have D(2, 0), E(4, 4) and F(4, 2)

AC= 2 units and DF= 2 units

AC≅DF

Length of segment AB.

A (0, 2) and B (2, 4)

Here, d=√[(x₂-x₁)²+(y₂-y₁)²]

= √[(2-0)²+(4-2)²]

= √8

AB = 2.83

Length of segment FD.

D (2, 0)

F (4, 2)

Here, d=√[(4-2)²+(2-0)²]

FD= = 2.83

AC≅FD

Triangle ABC is congruent to triangle FDE by SAS congruence

Hence, students did mistake in line 1.

To learn more about the congruent theorem visit:

https://brainly.com/question/24033497.

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