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Given: \( c \parallel d \)

Prove: \( m_c = m_d \)

Select the correct answer from each drop-down menu.

Statements
1. \( c \parallel d \)
2. \( c = m_c x + b_c \)
3. \( d = m_d x + b_d \)
4. \( m_c x + b_c = m_d x + b_d \)
5. \( m_c x - m_d x = b_d - b_c \)
6. \( x (m_c - m_d) = b_d - b_c \)
7. \( x = \frac{b_d - b_c}{m_c - m_d} \)
8. \( m_c - m_d = 0 \)
9. \( m_c = m_d \)

Reasons
1. Given
2. Write equations for lines \( c \) and \( d \)
3. Solve for \( x \)
4. Subtraction property of equality
5. Distributive property
6. Division property of equality
7. \( x \) does not exist; therefore, the denominator must be 0
8. Addition property of equality



Answer :

GinnyAnswer
Sure, let's go through the process step-by-step.

Given that \( c \| d \), this means that lines \( c \) and \( d \) are parallel.

To prove: \( m_c = m_d \)

Statements

1. \( c \| d \)
2. Equations for lines \( c \) and \( d \): \( c = m_c x + b_c \) and \( d = m_d x + b_d \)
3. Set the equations equal because \( c \parallel d \) implies that the slopes are the same: \( m_c x + b_c = m_d x + b_d \)
4. Subtract \( m_d x \) from both sides to isolate the terms containing \( x \): \( m_c x - m_d x = b_d - b_c \)
5. Factor out \( x \): \( x(m_c - m_d) = b_d - b_c \)
6. Solve for \( x \): \( x = \frac{b_d - b_c}{m_c - m_d} \)
7. Since \( c \parallel d \), \( x \) does not exist for any \( x \) in the real number line, meaning the denominator must be zero: \( m_c - m_d = 0 \)
8. Combine similar terms: \( m_c = m_d \)

Reasons

1. Given (c \|d)
2. Write equations for lines \( c \) and \( d \)
3. Given that \( c \parallel d \)
4. Subtraction property of equality
5. Distributive property
6. Division property of equality
7. \( x \) does not exist; therefore, the denominator must be 0
8. Addition property of equality

Thus, since [tex]\( c \| d \)[/tex], we have proved that [tex]\( m_c = m_d \)[/tex].

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