Question

Given: m∠ABE = m∠CBD

Prove: m∠ABD = m∠CBE

What is the reason for B ?
What is the reason for A ?
What is the reason for D?

Answer 1

Reason A - Given

Reason B - Angle Addition Postulate

Reason C - Substitution Property

Reason D - Subtraction Property

Explanation:

Given: m∠ABE = m∠CBD

Prove: m∠ABD = m∠CBE

1.
`m\angle ABE=m\angle CBD` - given (reason A)

2.
`m\angle ABE=m\angle ABD+m\angle DBE` - 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.
`m\angle CBD=m\angle CBE+m\angle DBE` - Angle Addition Postulate

4.
`m\angle ABD+m\angle DBE=m\angle CBE+m\angle DBE` - substitution property (reason C)

5.
`m\angle ABD=m\angle CBE` - subtraction property (reason D)