Question

Prove the theorem: In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. Given the facts RS ⊥ CD and AB || CD, drag and drop each reason next to the appropriate statement in order to prove the statement RS ⊥ AB.

Answer 1

The theorem requiring proof;

A transversal perpendicular to one of two parallel lines is also perpendicular to the other parallel line

The two column proof is as follows

Statement
`{}` Reason

RS ⊥ CD
`{}` Given

AB ║ CD
`{}` Given

The Slope of AB = The slope of CD
`{}` definition of parallel lines

The Slope of RS = -1/(The slope of CD)
`{}` definition of perpendicular lines

The Slope of RS = -1/(The slope of AB)
`{}` transitive property of equality

The Slope of RS = -1/(The slope of AB)
`{}` definition of perpendicular lines

RS ⊥ AB

Explanation: