Step-by-step explanation:
We know that B is the midpoint of line AD, So, it divides AD into two equal parts, and then segment AB will be congruent to BD. Additionally, a segment is congruent to itself, so BC is congruent to BC.
Finally, we also know that Angle ABC and Angle DBC are right angles and in consequence, they are congruent.
Therefore, by SAS (Side - Angle - Side), the triangles ABC and DBC are congruent.
Answer:
Then, the two-column proof is:
Statement 1. B is the midpoint of AB
Reason 1. Given
Statement 2. AB ≅ BD
Reason 2. Definition of midpoint
Statement 3. ∠ABC and ∠DBC are right angles
Reason 3. Given
Statement 4. ∠ABC ≅ ∠DBC
Reason 4. Definition of congruence (they have the same measure)
Statement 5. BC ≅ BC
Reason 5. Reflexive property of congruence
Statement 6. ΔABC ≅ ΔDBC
Reason 6. SAS ( Side - Angle - Side)