Question

Use the image to answer the question.

A triangle is labeled clockwise as upper F upper G upper H, with vertex F pointing left. Point upper I is marked at the midpoint of side upper F upper G. Point upper J is marked at the midpoint of side upper G upper H. A line connects upper I and upper J.

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 ∠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.”

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 “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 ∠JIF≅∠GFH
and the missing reason is “corresponding angles of similar triangles are congruent.”

Answer 1

Missing statement: ∠GJI ≅ ∠GHF

Missing reason: corresponding angles of similar triangles are congruent (from △IGJ ∼ △FGH).