Question

Fill in the missing statement and reason of the proof below.
Given: BD ~ CE, Prove: AB ~ FE.

Answer 1

The missing statement and reason of the proof are as follows:

Missing statement: AB ≅ FE

Missing reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

The complete proof is as follows:

1. BD ~ CE Given
2. ∠ACB≅∠FDE Similarity definition
3. AB ⊥ BE Given
4. EF ⊥ BE Similarity definition
5. ∠B is a right angle Definition of perpendicular lines
6. ∠E is a right angle Definition of perpendicular lines
7. △ABC≅△FED ASA (Angle-Side-Angle)
8. AB ≅ FE CPCTC

Therefore, the missing statement is that the segments AB and FE are congruent, and the reason is that the segments AB and FE are congruent because they are corresponding parts of congruent triangles.