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 7. m∠abd = 90° 7. subtraction property 8. 90° = m∠abd 8. symmetric property 9. m∠abc = m∠abd 9. 10. ∠abc ≅ ∠abd 10. definition of congruent angles definition of angle bisector segment addition property definition of congruent angles transitive property

Explanation:

Step1: Analyze the proof

We are given a proof about angles and need to identify the reason for a particular step. The key is to understand the properties used in angle - related proofs.

Step2: Identify the relevant property

In the proof, we go from showing that \(m\angle ABC = m\angle ABD\) to \(\angle ABC\cong\angle ABD\). By the definition of congruent angles, two angles are congruent if and only if their measures are equal.

Answer:

definition of congruent angles