Sage has already proved that IGJ ~ FGH. She is now attempting to prove that IJ || FH. Help her to construct a viable argument. What is the missing statement and reason in her proof?

Question

Statements Reasons
1. AIGJ~ AFGH 1. Given
2. 2.
3. IJ | FH 3. If corresponding angles are congruent, then lines are parallel
(1 point)
The missing statement is <JIF~<GFH and the missing reason is "CPCTC Theorem."
The missing statement is <GIJ~<GFH and the missing reason is "CPCTC Theorem."
The missing statement is <GJI~<GHF and the missing reason is "corresponding angles of similar triangles are congruent."
The missing statement is <JIF~<GFH and the missing reason is "corresponding angles of similar triangles are congruent."

Answer 1

To prove that segments IJ and FH are parallel, Sage needs to establish that the corresponding angles of the two similar triangles (IGJ and FGH) are congruent. This is a key step in using the properties of similar triangles to conclude that the lines are parallel.

Given that IGJ ~ FGH has been established, we know from the properties of similar triangles that the corresponding angles are congruent. Thus:

1. Statement: <GJI ~ <GHF (corresponding angles of similar triangles are congruent).

2. Reason: "Corresponding angles of similar triangles are congruent."

This leads directly to the conclusion that IJ || FH because if corresponding angles are congruent, then the lines are parallel.

Therefore, the correct option to fill in the blanks in the proof is:

• The missing statement is <GJI ~ <GHF
• The missing reason is "corresponding angles of similar triangles are congruent."