Question

each sheet of metal on a roof is perpendicular to the top line of the roof. what can you conclude about the relationship between the sheets of roofing? justify your answer.
the sheets of metal are all parallel to each other by the alternate interior angles theorem.
the sheets of metal are all parallel to each other because in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
the sheets of metal are all parallel to each other because in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
the sheets of metal are all parallel to each other by the transitive property of parallel lines.

Explanation:

In a plane, when multiple lines (sheets of metal) are perpendicular to the same line (top - line of the roof), the property that two lines perpendicular to the same line are parallel to each other applies. The Alternate Interior Angles Theorem is about angles formed by a transversal and parallel lines and not relevant here. The property about a line being perpendicular to one of two parallel lines is the converse - we start with the perpendicularity to a single line and conclude parallelism of other lines. The Transitive Property of Parallel Lines is about if \(a\parallel b\) and \(b\parallel c\) then \(a\parallel c\), which is not the main concept here.

Answer:

The sheets of metal are all parallel to each other because in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.