The first hill of the steel dragon 2000 roller coaster in nagashima, japan, drops riders from a height of 318 ft. a portion of this first hill has been transposed onto a coordinate plane and is shown to the right.

1. the structure of the supports for the hill consists of steel beams that
run parallel and perpendicular to one another. the endpoints of the
beam shown by bc are (0, 150) and (120,0). the endpoints of the beam
shown by ad are (0, 125) and (100,0).

a. verify and explain why the two beams are parallel.

b. if angle dab = 125°, what is the measure of angle cba? justify your
reasoning

2. determine the equations of the lines containing the beams from item 1,
and explain how the equations of the lines can you determine that the beams are parallel.

3. a third support beam is perpendicular to the beam shown by bc. if marked on the coordinate plane, the line containing this beam would
pass through the point (60,75). what is the equation of the line containing this third beam? explain how you determined your answer.

the diagram below shows a section of the steel support structure of a roller coaster. 

use the diagram for items 4-6.
4. given jk || pl, measure of angle jkl = (10x + 5)º and angle plk = (12x - 1)º, what is
the measure, in degrees, of angle jkl and angle plk? explain how you determined your answer.
5. explain how an engineer could determine whether pn || lm by measuring two angles in the diagram.
6. write a two-column proof.
given: jk || pl, angle 1 is congruent to angle 2
prove: angle 3 is congruent to angle 4