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The proof below may or may not be correct. If the proof is incorrect, determine the first step number that is not justified and the reason it is not justified.
Given: triangle, A, C, F, \cong, triangle, B, D, F, comma△ACF≅△BDF, start overline, F, A, end overline, is perpendicular to, start overline, D, B, end overline
FA
⊥
DB
and start overline, F, B, end overline, is perpendicular to, start overline, A, C, end overline, .
FB
⊥
AC
.
Prove: triangle, A, D, B, \cong, triangle, B, C, A△ADB≅△BCA.
.... The diagram associated with this problem is located below the proof table, and is available as a tactile printout. There may be a clarifying note below the diagram.
Step Statement Reason
1
triangle, A, C, F, \cong, triangle, B, D, F△ACF≅△BDF
start overline, F, A, end overline, is perpendicular to, start overline, D, B, end overline
FA
⊥
DB
start overline, F, B, end overline, is perpendicular to, start overline, A, C, end overline
FB
⊥
AC
Given
2
start overline, A, C, end overline, \cong, start overline, B, D, end overline
AC
≅
BD
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
3
angle, A, D, B∠ADB is a right angle
Perpendicular lines form right angles
4
triangle, A, D, B△ADB is a right triangle
The triangle contains a right angle
5
triangle, B, C, A△BCA is a right triangle
The triangle contains a right angle
6
start overline, A, B, end overline, \cong, start overline, A, B, end overline
AB
≅
AB
Reflexive Property
7
triangle, A, D, B, \cong, triangle, B, C, A△ADB≅△BCA
HL
A
B
C
D
E
F
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Note: start overline, F, B, end overline, comma
FB
, start overline, A, C, end overline, comma
AC
, start overline, D, B, end overline
DB
and start overline, A, F, end overline
AF
are segments.
Answer
Attempt 1 out of 2
The proof is
incorrect
and step number
is the first unjustified step due to a
1 answer
The proof is incorrect and step number 2 is the first unjustified step due to a misapplication of CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
While triangles \( \triangle ACF \) and \( \triangle BDF \) are given to be congruent, the segments \( AC \) and \( BD \) are not necessarily corresponding parts because the triangles share a vertex \( F \) and the relation between the triangles does not imply direct correspondence between those specific sides. Therefore, the conclusion that \( AC \cong BD \) from the given congruence is not valid.
