Question

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?

Complete the Table to Prove Two Given Lines Are Parallel
Statements Reasons
1. △IGJ∼△FGH
1. Given
2. 2.
3. IJ¯¯¯¯¯¯∥FH¯¯¯¯¯¯¯¯
3. If corresponding angles are congruent, then lines are parallel
(1 point)
Responses

The missing statement is ∠GJI≅∠GHF
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 ∠JIF≅∠GFH
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 ∠JIF≅∠GFH
and the missing reason is “CPCTC Theorem.”
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 “CPCTC Theorem.”

The missing statement is ∠GIJ≅∠GFH
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.”
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Answer 1

Answer: Step 2: ∠GJI ≅ ∠GHF. Reason: corresponding angles of similar triangles are congruent.

Explanation: From △IGJ ∼ △FGH corresponding angles are congruent, so the angle formed by GJ and JI equals the angle formed by GH and HF. Those are corresponding angles; if corresponding angles are congruent, the lines IJ and FH are parallel.