Proving Similar Triangles Quick Check 4 of 54 of 5 Items Question Use the image to answer the 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? 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 “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.” Skip to navigation page 23 of 23 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

asked by lo

3 months ago

17 views

0

0

1 answer

To prove that $ IJ \parallel FH $ given that $ \triangle IGJ \sim \triangle FGH $, we can use the fact that corresponding angles of similar triangles are congruent.

From the similarity of triangles $ \triangle IGJ \sim \triangle FGH $, we know that:

$ \angle GJI $ corresponds to $ \angle GHF $

$ \angle GIJ $ corresponds to $ \angle GFH $

$ \angle IGJ $ corresponds to $ \angle HFG $

To use this information to prove that $ IJ \parallel FH $, we need to show that either of the pairs of corresponding angles is congruent.

The missing statement in Sage's proof is:

$ \angle GIJ \cong \angle GFH $

And the reason would be:

"Corresponding angles of similar triangles are congruent."

Thus, the appropriate choice from the provided options would be:

The missing statement is $ \angle GIJ \cong \angle GFH $ and the missing reason is "corresponding angles of similar triangles are congruent."

This demonstrates that because the corresponding angles are congruent, the lines $ IJ $ and $ FH $ must be parallel.

answered by GPT-4o mini

0

0

Ask a New Question or answer this question.

Question

Proving Similar Triangles Quick Check 4 of 54 of 5 Items Question Use the image to answer the 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? 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 “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.” Skip to navigation page 23 of 23 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

1 answer

To prove that $ IJ \parallel FH $ given that $ \triangle IGJ \sim \triangle FGH $, we can use the fact that corresponding angles of similar triangles are congruent.

From the similarity of triangles $ \triangle IGJ \sim \triangle FGH $, we know that:

$ \angle GJI $ corresponds to $ \angle GHF $
$ \angle GIJ $ corresponds to $ \angle GFH $
$ \angle IGJ $ corresponds to $ \angle HFG $

To use this information to prove that $ IJ \parallel FH $, we need to show that either of the pairs of corresponding angles is congruent.

The missing statement in Sage's proof is:

$ \angle GIJ \cong \angle GFH $

And the reason would be:

"Corresponding angles of similar triangles are congruent."

Thus, the appropriate choice from the provided options would be:

The missing statement is $ \angle GIJ \cong \angle GFH $ and the missing reason is "corresponding angles of similar triangles are congruent."

This demonstrates that because the corresponding angles are congruent, the lines $ IJ $ and $ FH $ must be parallel.

Ask a New Question or answer this question.

GPT-4o mini · Answer

To prove that $ IJ \parallel FH $ given that $ \triangle IGJ \sim \triangle FGH $, we can use the fact that corresponding angles of similar triangles are congruent. From the similarity of triangles $ \triangle IGJ \sim \triangle FGH $, we know that: - $ \angle GJI $ corresponds to $ \angle GHF $ - $ \angle GIJ $ corresponds to $ \angle GFH $ - $ \angle IGJ $ corresponds to $ \angle HFG $ To use this information to prove that $ IJ \parallel FH $, we need to show that either of the pairs of corresponding angles is congruent. The missing statement in Sage's proof is: - $ \angle GIJ \cong \angle GFH $ And the reason would be: - "Corresponding angles of similar triangles are congruent." Thus, the appropriate choice from the provided options would be: - The missing statement is $ \angle GIJ \cong \angle GFH $ and the missing reason is "corresponding angles of similar triangles are congruent." This demonstrates that because the corresponding angles are congruent, the lines $ IJ $ and $ FH $ must be parallel.