Answer:
8. parallel
9. not parallel
Explanation:
Segment ST will be parallel to base segment PR if the sides of the triangle are divided proportionally.
8.
We can compare the whole to the short part:
102/45 ?? (41.8 +33)/33
2.266... = 74.8/33 = 2.266...
The sides are proportional, so the segments are parallel.
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9.
We can compare the longer portion to the shorter portion.
38/19 ?? 52/24
2 ≠ 2 1/6
The sides are not proportional, so the segments are not parallel.
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Additional comment
Here, we compared segment lengths on the same side of the triangle. You can also compare segment lengths on opposite sides of the triangle. For example, in 9, you could look at any of the relations ...
19/24 vs 38/52
19/(19+38) vs 24/(24+52)
or the inverse of these:
24/19 vs 52/39, for example