Question

complete the proof by choosing the correct
eason\.
given: ( m angle cbe = m angle fbh )
( m angle 1 = m angle 3 )
prove: ( m angle 2 = m angle 4 )
1 ( m angle cbe = m angle 1 + m angle 2 )
reason?
2 ( m angle fbh = m angle 3 + m angle 4 )
reason?
3 ( m angle cbe = m angle fbh )
reason?
4 ( m angle 1 + m angle 2 = m angle 3 + m angle 4 )
reason?
5 ( m angle 1 = m angle 3 )
reason?
6 ( m angle 3 + m angle 2 = m angle 3 + m angle 4 )
reason?
7 ( m angle 2 = m angle 4 )
reason?

Explanation:

Step1: Substitute \(m\angle1 = m\angle3\) into \(m\angle CBE=m\angle1 + m\angle2\)

Since \(m\angle CBE=m\angle1 + m\angle2\) and \(m\angle1 = m\angle3\), we get \(m\angle CBE=m\angle3 + m\angle2\) by substitution property of equality.

Step2: Use the given \(m\angle CBE=m\angle FBH\)

Given \(m\angle CBE=m\angle FBH\), so \(m\angle FBH=m\angle3 + m\angle2\) (transitive property of equality: if \(a = b\) and \(b = c\), then \(a = c\), here \(a=m\angle FBH\), \(b = m\angle CBE\), \(c=m\angle3 + m\angle2\))

Step3: Substitute \(m\angle1 = m\angle3\) into \(m\angle FBH=m\angle3 + m\angle2\)

If \(m\angle1 = m\angle3\), then \(m\angle FBH=m\angle1 + m\angle2\) (substitution property of equality)

Step4: Rearrange the equation \(m\angle FBH=m\angle1 + m\angle2\)

We know that \(m\angle FBH=m\angle1 + m\angle2\). Also, if we consider the angle - addition postulate, and given \(m\angle1 = m\angle3\), we can rewrite it. Since \(m\angle1 + m\angle2=m\angle3 + m\angle2\) (because \(m\angle1 = m\angle3\)), and \(m\angle CBE=m\angle FBH\)

Step5: Use the given \(m\angle1 = m\angle3\) for another substitution

We want to prove \(m\angle2 = m\angle4\). We know that \(m\angle CBE=m\angle1 + m\angle2\) and \(m\angle FBH=m\angle3 + m\angle4\). Since \(m\angle CBE=m\angle FBH\) and \(m\angle1 = m\angle3\), by subtraction property of equality (\(m\angle CBE−m\angle1=m\angle FBH - m\angle3\)), we get \(m\angle2 = m\angle4\)

Answer:

1. Angle - addition postulate
2. Substitution property (using \(m\angle CBE=m\angle FBH\))
3. Substitution property (using \(m\angle1 = m\angle3\))
4. Angle - addition postulate
5. Substitution property (using \(m\angle1 = m\angle3\))
6. Angle - addition postulate
7. Subtraction property of equality (If \(a=b\) and \(c = d\), then \(a - c=b - d\), here \(a=m\angle CBE\), \(b=m\angle FBH\), \(c=m\angle1\), \(d=m\angle3\))