Let's draw a diagram and highlight the segments we are asked to compare.
Now we will identify congruent segments in the triangles corresponding to the different positions of the crane's arm.
Congruent Segments
Justification
PN≅TS
Both segments represent the same fixed part of the crane.
MP≅RT
Given. Both segments represent the arm of the crane in different positions.
Using the measures on the diagram, we can compare angles ∠ NPM and ∠ STR.
52>29
⇓
m ∠ NPM>m ∠ STR
Since triangles △ NPM and △ STR have two pairs of congruent sides, the Hinge Theorem allows us to compare the third sides.
m ∠ NPM>m ∠ STR
⇓
MN> RS
Segment RS is shorter.
