Question

Complete the two-column the proof by writing the appropriate reason for each statement.

Given: m∠1 = m∠3

Prove: m∠EBA = m∠CBD


Reasons (one is used twice): Angle Addition Postulate, Commutative Property of Addition, Substitution, Transitive Property


Answer:


1. Statement: m∠1 = m∠3

1. Reason: Given


2. Statement: m∠EBA = m∠2 + m∠3

2. Reason: ___________


3. Statement: m∠EBA = m∠2 + m∠1

3. Reason: ___________


4. Statement: m∠EBA = m∠1 + m∠2

4. Reason: ___________


5. Statement: m∠1 + m∠2 = m∠CBD

5. Reason: ___________


6. Statement: m∠EBA = m∠CBD

6. Reason: ___________

Answer 1

The required Prove is shown below.

Explanation:

Consider the provided proof.

The angle addition postulate states that if C is in the interior of AOB , then

m∠AOC+m∠COB=m∠AOB

Transitive property of equality: If a = b and b = c, then a = c.

Substitution property: If x = y, then one can replace x with y.

Commutative property of addition: a + b = b + a

Now use above property to prove m∠EBA = m∠CBD

Statement: Reason:

m∠1 = m∠3 Given

m∠EBA = m∠2 + m∠3 Angle Addition Postulate

m∠EBA = m∠2 + m∠1 Substitution Property of Equal

m∠EBA = m∠1 + m∠2 Commutative Property of Addition

m∠1 + m∠2 = m∠CBD Angle Addition Postulate

m∠EBA = m∠CBD Transitive Property of Equality

Hence, the required Prove is shown above.