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

Answer:

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

Step-by-step explanation: