Sage has already proved that

Question

Sage has already proved that 
△
I
G
J
∼
△
F
G
H
. She is now attempting to prove that 
¯¯¯¯¯¯
I
J
∥
¯¯¯¯¯¯¯¯¯
F
H
. Help her to construct a viable argument. What is the missing statement and reason in her proof?

Statements	Reasons
1. 
△
I
G
J
∼
△
F
G
H
1. Given
2. 	2. 
3. 
¯¯¯¯¯¯
I
J
∥
¯¯¯¯¯¯¯¯¯
F
H
3. If corresponding angles are congruent, then lines are parallel (1 point)
Responses

The missing statement is  
∠
G
I
J
≅
∠
G
F
H
  and the missing reason is “CPCTC Theorem.” 
The missing statement is  angle upper G upper I upper J congruent to angle upper G upper F upper H  and the missing reason is “CPCTC Theorem.”

The missing statement is 
∠
G
J
I
≅
∠
G
H
F
 and the missing reason is “corresponding angles of similar triangles are congruent.” 
The missing statement is  angle upper G upper J upper I congruent to angle upper G upper H upper F  and the missing reason is “corresponding angles of similar triangles are congruent.”

The missing statement is 
∠
J
I
F
≅
∠
G
F
H
 and the missing reason is “corresponding angles of similar triangles are congruent.” 
The missing statement is  angle upper J upper I upper F congruent to angle upper G upper F upper H  and the missing reason is “corresponding angles of similar triangles are congruent.”

The missing statement is 
∠
J
I
F
≅
∠
G
F
H
 and the missing reason is “CPCTC Theorem.”

GPT-4o mini · Answer

To prove that line segments $ \overline{IJ} $ and $ \overline{FH} $ are parallel based on the given triangles, we can use the fact that corresponding angles are congruent when two angles are formed by a transversal intersecting parallel lines. Since Sage has already proven that triangles $ \triangle IGJ $ and $ \triangle FGH $ are similar, we know that their corresponding angles are congruent. Thus, the missing statement and reason in Sage's proof are: **Missing Statement:** $ \angle GJI \cong \angle GHF $ **Missing Reason:** "Corresponding angles of similar triangles are congruent." Hence the correct response is: The missing statement is $ \angle GJI \cong \angle GHF $ and the missing reason is "corresponding angles of similar triangles are congruent."