Question

1. \\( \angle abc \\) is a right angle
2. \\( \angle dbc \\) is a straight angle
3. \\( m \angle abc = 90 ^ { \circ } \\)
4. \\( m \angle dbc = 180 ^ { \circ } \\)
5. \\( m \angle abd + m \angle abc = m \angle dbc \\)
6. \\( m \angle abd + 90 ^ { \circ } = 180 ^ { \circ } \\)
7. \\( m \angle abd = 90 ^ { \circ } \\)
8. \\( \angle abd \\) is a right angle
9. given
10. given
11. definition of right angle
12. definition of straight angle
13. angle addition property
14. substitution property
15. subtraction property
16. definition of right angle

Explanation:

Step1: Analyze the proof structure

The given statements and reasons are presented in a two - column format (statements in one column and reasons in another). This is a characteristic of a two - column proof. In a two - column proof, each step of the logical argument (statement) is paired with its corresponding justification (reason).

Step2: Compare with other proof types

• A one - paragraph proof would present the entire argument in a continuous text paragraph without the separation of statements and reasons into columns.
• A flowchart proof uses arrows and boxes to show the flow of logical reasoning, which is not the case here.
• A two - paragraph proof is not a standard proof format in geometry compared to the well - known two - column, flowchart, and paragraph (one - paragraph) proofs.

Answer:

Two - column proof.