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.

Solution Steps

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.

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.

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

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