Questions: Lines x and y are parallel. Write an equation that represents the relationship between b and e. Explain how you know this equation is always true.

Lines x and y are parallel. Write an equation that represents the relationship between b and e. Explain how you know this equation is always true.
Transcript text: Lines $x$ and $y$ are parallel. Write an equation that represents the relationship between $b$ and $e$. Explain how you know this equation is always true.
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Solution

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Solution Steps

Step 1: Identify the given information

The problem states that lines x and y are parallel. We need to write an equation that represents the relationship between angles b and e and explain why this equation is always true.

Step 2: Understand the relationship between angles

Since lines x and y are parallel, the corresponding angles formed by a transversal are equal. In the diagram, angles b and e are corresponding angles.

Step 3: Write the equation

Since corresponding angles are equal when lines are parallel, we can write the equation: \[ b = e \]

Step 4: Explain why the equation is always true

The equation \( b = e \) is always true because, by the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then each pair of corresponding angles is equal.

Final Answer

\[ b = e \]

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