given
$m\angle1 + m\angle2 = 120^{circ}$
$m\angle3 + m\angle4 = 120^{circ}$
$\angle2\cong\angle3$
prove
$\angle1\cong\angle4$
statement
1) $m\angle1 + m\angle2 = 120^{circ}$
2) $m\angle3 + m\angle4 = 120^{circ}$
3) $m\angle1 + m\angle2 = m\angle3 + m\angle4$
4) $\angle2\cong\angle3$
5) $m\angle2 = m\angle3$
6) $m\angle1 + m\angle2 = m\angle2 + m\angle4$
7) $m\angle1 = m\angle4$
8) $\angle1\cong\angle4$
reason
1) given
2) given
3) substitution
4) given
5) definition of congruency
6) ?
7) ?
8) definition of congruency

Question

Accepted Answer

# Explanation:
## Step1: Analyze the equality in statement 6
From statement 5, we know $m\angle2 = m\angle3$. In statement 3, $m\angle1 + m\angle2=m\angle3 + m\angle4$. Substituting $m\angle2$ for $m\angle3$ (since they are equal), we get $m\angle1 + m\angle2=m\angle2 + m\angle4$. This is based on the substitution property.
## Step2: Analyze the equality in statement 7
We have $m\angle1 + m\angle2=m\angle2 + m\angle4$. Subtracting $m\angle2$ from both sides of the equation $m\angle1 + m\angle2=m\angle2 + m\angle4$ (using the subtraction property of equality: if $a + b=c + b$, then $a=c$), we get $m\angle1=m\angle4$.

# Answer:
6) Substitution Property; 7) Subtraction Property of Equality

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze the equality in statement 6

Step2: Analyze the equality in statement 7

Answer: