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. definition of congruent angles 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 that ∠ABC is a right - angle and ∠DBC is a straight - angle. Using angle addition property, we set up an equation involving ∠ABD, ∠ABC, and ∠DBC. Then we use substitution, subtraction, symmetric properties to show that m∠ABC = m∠ABD.

Step2: Recall the key concept

The step from m∠ABC = m∠ABD to ∠ABC≅∠ABD is based on the definition of congruent angles which states that two angles are congruent if and only if they have the same measure.

Answer:

definition of congruent angles