Given the diagram, determine whether line OS is parallel to line PT.

Cem Hayes 2021-08-11 Answered
Given the diagram, determine whether line OS is parallel to line PT.
image
1.yes, parallel
2.unable to determine
3.no, not parallel

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Expert Answer

unett
Answered 2021-08-12 Author has 10896 answers

Solution:
TP would be parallel to SQ if and only if the angle \(\displaystyle\angle{T}{P}{R}\stackrel{\sim}{=}\angle{S}{Q}{R}\)
To prove the, we shall use the similarity between the triangle TPR and SQR.
Using the property of similarity, if the the two triangles are similar, then,
\(\displaystyle{\frac{{{T}{S}}}{{{S}{R}}}}={\frac{{{P}{Q}}}{{{Q}{R}}}}\)
Now we shall check this by putting the values given, we get,
\(\displaystyle{\frac{{{34}}}{{{15}}}}\ne{\frac{{{35}}}{{{16}}}}\)
Hence the line are not parallel.
Answer: (3) no, not parallel.

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