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 ∠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 ∠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 ∠GIJ≅∠GFH
and the missing reason is “CPCTC Theorem.”

Answer 1

Missing statement: ∠GJI ≅ ∠GHF

Missing reason: Corresponding angles of similar triangles are congruent.

Explanation: From △IGJ ∼ △FGH, angle J corresponds to angle H, so ∠GJI ≅ ∠GHF. Those are corresponding angles formed by transversal GJ/GH with lines IJ and FH; since corresponding angles are congruent, IJ ∥ FH.