Question

Which statement is not used to prove that ΔFGH is similar to ΔFIJ?

A. Angle F is congruent to itself, due to the reflexive property.

B. Angles FJI and FHG are congruent, due to the corresponding angles postulate.

C. Points F, J, and H are collinear.

D. Segments JI and HG are parallel.

Answer 1

To prove that ΔFGH is similar to ΔFIJ, we need to use statements that establish the corresponding angles and proportional sides of the triangles. Option A is not used to prove the similarity of the triangles.

Step-by-step explanation:

To prove that ΔFGH is similar to ΔFIJ, we need to use statements that establish the corresponding angles and proportional sides of the triangles. Let's analyze each option:

A. Angle F is congruent to itself, due to the reflexive property. This statement is not relevant for proving similarity.

B. Angles FJI and FHG are congruent, due to the corresponding angles postulate. This statement establishes a correspondence between angles and is useful for proving similarity.

C. Points F, J, and H are collinear. This statement is not relevant for proving similarity.

D. Segments JI and HG are parallel. This statement establishes a correspondence between sides and is useful for proving similarity.

Based on the analysis, option A is not used to prove the similarity of the triangles.

Answer 2

C. Points F, J, and H are collinear.

Step-by-step explanation:

Given

See attachment for triangle

Required

Which statement is false

Options A, B and D are true while C is false.

Two points are said to collinear if a straight line can pass through them.

From the attached triangle, we can see that a straight line cannot pass through F, J and H.

Hence, they are not collinear.

Since the statement is false, then it cannot be used as part of the proof.