Answer:
Reason A - Given
Reason B - Angle Addition Postulate
Reason C - Substitution Property
Reason D - Subtraction Property
Step-by-step explanation:
Given: m∠ABE = m∠CBD
Prove: m∠ABD = m∠CBE
1. [tex]m\angle ABE=m\angle CBD[/tex] - given (reason A)
2. [tex]m\angle ABE=m\angle ABD+m\angle DBE[/tex] - Angle Addition Postulate (reason B)
Angle Addition Postulate states that the measure of an angle formed by two angles side by side is the sum of the measures of the two angles.
3. [tex]m\angle CBD=m\angle CBE+m\angle DBE[/tex] - Angle Addition Postulate
4. [tex]m\angle ABD+m\angle DBE=m\angle CBE+m\angle DBE[/tex] - substitution property (reason C)
5. [tex]m\angle ABD=m\angle CBE[/tex] - subtraction property (reason D)
