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

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

1.yes, parallel
2.unable to determine
3.no, not parallel

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unett

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.