Question

Use the figure below to answer the question that follows:

What must be given to prove that ABIJ~ ABDF? (6 points)

Answer 1

To prove that ABIJ ~ ABDF, we must show that the corresponding angles are congruent and the corresponding sides are proportional.

From the figure, we can see that:

- ∠ABI ≅ ∠DBF (corresponding angles)

- ∠BAI ≅ ∠FBD (corresponding angles)

- ∠ABJ ≅ ∠DFB (corresponding angles)

To show that the corresponding sides are proportional, we can use the following ratios:

- AB/AB = 1 (common side)

- AI/DF = 2/3 (given)

- BJ/BF = 2/3 (given)

Therefore, if we can prove that the corresponding angles are congruent and the corresponding sides are proportional, we can conclude that ABIJ ~ ABDF.

Explanation: