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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: EE is the midpoint of start overline, B, D, end overline
BD
and angle, A, B, C, \cong, angle, C, D, F, .∠ABC≅∠CDF.
Prove: start overline, B, D, end overline, is perpendicular to, start overline, C, E, end overline
BD
⊥
CE
.
.... 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
EE is the midpoint of start overline, B, D, end overline
BD
angle, A, B, C, \cong, angle, C, D, F∠ABC≅∠CDF
Given
2
angle, C, D, F∠CDF and angle, C, D, E∠CDE are supplementary
If two angles form a linear pair, then they are supplementary
3
angle, C, B, E, \cong, angle, C, D, E∠CBE≅∠CDE
If two angles are supplements of the same angle (or congruent angles), then they are congruent
4
start overline, B, C, end overline, \cong, start overline, D, C, end overline
BC
≅
DC
In a triangle, sides opposite of congruent angles are congruent
5
start overline, B, E, end overline, \cong, start overline, E, D, end overline
BE
≅
ED
A midpoint divides a segment into two congruent segments
6
triangle, B, C, E, \cong, triangle, D, C, E△BCE≅△DCE
SAS
7
angle, C, E, B, \cong, angle, C, E, D∠CEB≅∠CED
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
8
start overline, B, D, end overline, is perpendicular to, start overline, C, E, end overline
BD
⊥
CE
If two lines form a linear pair of congruent angles, then the lines are perpendicular
A
B
C
D
E
F
An image is shown. To download tactile, press SHIFT-CONTROL-U for UEB or SHIFT-CONTROL-E for Nemeth.
Note: the segment A, FAF is a straight segment.
Answer
Attempt 1 out of 2
The proof is
incorrect
and step number
is the first unjustified step due to a
missing prior step
. Submit Answer
1 answer
The proof is incorrect and step number 2 is the first unjustified step due to a missing prior step.
Reason: The statement in step 2 claims that angles \( \angle CDF \) and \( \angle CDE \) are supplementary based on the assertion that they form a linear pair. However, without proper justification or a clear indication that they indeed form a linear pair, this statement cannot be considered valid. There needs to be a clear geometric argument or figure supporting the assertion that these angles are adjacent and creating a straight angle.
