Which statement is not used to prove that ΔFGH is similar to ΔFIJ?
triangles FGH and FIJ in which point I is between points F and G on segment FG and point J is between points F and H on segment FH
Angle F is congruent to itself, due to the reflexive property.
Angles FJI and FHG are congruent, due to the corresponding angles postulate.
Points F, J, and H are collinear.
Segments JI and HG are parallel.
To determine which statement is not used to prove that ΔFGH is similar to ΔFIJ, let's go through each statement and see if it is relevant to proving the similarity.
1. Angle F is congruent to itself, due to the reflexive property.
This statement is not relevant to proving the similarity between the triangles. The reflexive property only applies to congruent angles within the same triangle, not between different triangles. Therefore, this statement is likely not used to prove the similarity.
2. Angles FJI and FHG are congruent, due to the corresponding angles postulate.
This statement is valid for proving the similarity of the triangles. According to the corresponding angles postulate, if two angles in one triangle are congruent to two angles in another triangle, then the triangles are similar. Therefore, this statement is likely used to prove the similarity.
3. Points F, J, and H are collinear.
This statement is not relevant to proving the similarity between the triangles. Collinearity of the points does not by itself establish similarity.
4. Segments JI and HG are parallel.
This statement is also valid for proving the similarity of the triangles. If corresponding sides of two triangles are proportional and parallel, then the triangles are similar. Therefore, this statement is likely used to prove the similarity.
Based on the analysis, the statement that is not used to prove that ΔFGH is similar to ΔFIJ is:
Points F, J, and H are collinear.
Note: It is possible that there may be other statements or properties used in the actual proof of the similarity that is not listed here.