Question

statements reasons

1. ∠abc is a right angle 1 given

2 ∠dbc is a straight angle 2 given
3 m∠abc = 90° 3 definition of right angle
4 m∠dbc = 180° 4 definition of straight angle
5 m∠abd + m∠abc = m∠dbc 5 angle addition property
6 m∠abd + 90° = 180° 6 substitution property

1. m∠abd = 90° 7 subtraction property
2. ∠abd is a right angle 8 definition of right angle

two - column prooftwo - paragraph proofflowchart proofone - paragraph proof

Explanation:

A two - column proof is a method of presenting a logical argument in geometry. It has two columns: one for statements (such as geometric facts, like angles being right or straight angles) and one for the reasons (such as definitions, given information, or properties) that justify those statements. In the given table, we have statements about angles (e.g., \( \angle ABC\) is a right angle, \(m\angle ABC = 90^{\circ}\)) in one column and their corresponding justifications (e.g., given, definition of right angle) in the other column. A two - paragraph proof would have two separate paragraphs (one for a set of related statements and their reasons, and another for another set). A flowchart proof uses boxes and arrows to show the flow of the logical argument. A one - paragraph proof would present all the statements and reasons in a single paragraph.

Answer:

two - column proof