Question

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 problem context

We are given statements and reasons about angles and need to identify the reason for a particular step.

Step2: Identify the key step

The step from $m\angle ABC = m\angle ABD$ to $\angle ABC\cong\angle ABD$ is based on the concept of congruent - angle definition.

Answer:

definition of congruent angles