Proving Lines that are Parallel or Perpendicular

Edit:   The program seems to have taken a dislike to me using a less thant sign for a angle sign.

Chunks of my solution have disappeared.    Bummer!

Maybe you can fill in some of the blanks yourself.  The first part was easy.

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1)

becasue;

If two lines are cut by a tranversal and the resulting co-interior anges are supplementary then the 2 lines must be parallel.

2)

L3 is parallel to L1

and QT is perpendicular to L3

so QT is perpendicular to L1 s

so angle PQT  = 90 degrees.

RP is perpendicular to QT   given

so     

triangle QSP and triangle RPS are similar  (2 equal angles)

so the the third angles must also be equal   

so   

so   

so  QT is perpendicular to L2

.