Question

Given: mz1+ m2 = 120°, mz3+ m24 = 120°,

and 22 = 23
Prove: 21 = 24
Reason:
Statement:
1. mz1+ m2 = 120°
1. Given
2. mz3+ m24 = 120°
2. Given
3. mz1+mz2 = mz3+ m24 3. Substitution
4.22 = 23
4. Given
5. m/2=m23
5. Definition of
Congruency
6. mz1 + m2 = mz2+ m24 6.[? ]
7. m/1=m24 [?]
8. 21 = 24
8. Definition of
Congruency
Select the reason that best supports
Statement 6 and 7 in the given proof.

Answer 1

the best reason that supports Statement 6 and 7 in the given proof is Transitive Property of Equality.

Explanation:

Given the proof, statement 6 is mz1 + m2 = mz2 + m24 and statement 7 is m/1 = m24. To prove these statements, we can use the following reasoning:

mz1 + m2 = 120° (Given)

mz3 + m24 = 120° (Given)

mz1 + mz2 = mz3 + m24 (Substitution)

22 = 23 (Given)

m/2 = m23 (Definition of Congruency)

mz1 + m2 = mz2 + m24 12 (Transitive Property of Equality)

m/1 = m24 12 (Substitution)