Chapter 3.5, Problem 36PPS

(a)

To determine

Draw three sets of parallel lines k and l, s and t, and x and y. Draw shortest segment $\overline{BC}$ and label points A and D .

Explanation of Solution

Calculation :

The three sets are :

  

(b)

To determine

Complete the table.

Explanation of Solution

Calculation :

Since the segment $\overline{BC}$ is the shortest distance between the parallel lines , it is perpendicular to the parallel lines.Hence the angles are right angles:

Set of parallel lines	$m\angle ABC$	$m\angle BCD$
k and l	$90°$	$90°$
s and t	$90°$	$90°$
x and y	$90°$	$90°$

(c)

To determine

Make a conjecture about the angle that the shortest segment forms with the parallel lines.

Answer to Problem 36PPS

  $90°$

Explanation of Solution

Calculation :

From part (b) , we have that the angle the shortest segment forms with the parallel lines is $90°$ .