Question
Sage has already proved that Triangle IGJ ~ Triangle FGH. She is now attempting to prove that line IJ || line FH. Help her to construct a viable argument. What is the missing statement and reason in her proof?
Statements: 1. Triangle IGJ ~ Triangle FGH 2. [Blank] 3. Line IJ || Line FH
Reasons: 1. Given 2. [Blank] 3. If corresponding angles are congruent, then lines are parallel
Statements: 1. Triangle IGJ ~ Triangle FGH 2. [Blank] 3. Line IJ || Line FH
Reasons: 1. Given 2. [Blank] 3. If corresponding angles are congruent, then lines are parallel
Answers
GPT-4o mini
To complete Sage's proof and establish that line IJ is parallel to line FH, we need to fill in the missing statement and reason based on the properties of similar triangles.
Here's how the argument can be constructed:
**Statements:**
1. Triangle IGJ ~ Triangle FGH
2. Angle IGJ ≅ Angle FGH (corresponding angles of similar triangles)
3. Line IJ || Line FH
**Reasons:**
1. Given
2. Corresponding angles of similar triangles are congruent
3. If corresponding angles are congruent, then lines are parallel
By showing that angle IGJ is congruent to angle FGH based on the similarity of the triangles, she can conclude that the lines IJ and FH are parallel.
Here's how the argument can be constructed:
**Statements:**
1. Triangle IGJ ~ Triangle FGH
2. Angle IGJ ≅ Angle FGH (corresponding angles of similar triangles)
3. Line IJ || Line FH
**Reasons:**
1. Given
2. Corresponding angles of similar triangles are congruent
3. If corresponding angles are congruent, then lines are parallel
By showing that angle IGJ is congruent to angle FGH based on the similarity of the triangles, she can conclude that the lines IJ and FH are parallel.