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Hello! I'm struggling to prove this problem. Can someone please help me how to solve it? 

 

 Apr 12, 2022

Best Answer 

 #1
avatar+117180 
+2

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.

-----------------

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

.

 Apr 12, 2022
edited by Melody  Apr 12, 2022
 #1
avatar+117180 
+2
Best Answer

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.

-----------------

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

.

Melody Apr 12, 2022
edited by Melody  Apr 12, 2022

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