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In the diagram, P, Q, R, S, and T are collinear. PT=54 QT= 42 QS= 31 and RS= 17. Then find PQ, QR, ST, PS, PR, RT

In The Diagram P Q R S And T Are Collinear PT54 QT 42 QS 31 And RS 17 Then Find PQ QR ST PS PR RT class=

Answer :

   If the points like P, Q, R, S and T are collinear they will follow the segment addition postulate.

  Length of segments will be,

 PQ = 12 units

 QR = 14 units

 ST = 11 units

 PS = 43 units

 PR = 26 units

 RT = 28 units

It's given in the question,

  • P, Q, R, S, T are collinear.

And the lengths of different segments are,

  • PT = 54
  • QT = 42
  • QS = 31
  • RS = 17

By segment addition postulate,

PQ + QT = PT

PQ = PT - QT

PQ = 54 - 42

     = 12 units

QR + RS = QS

QR = QS - RS

     = 31 - 17 = 14 units

ST = QT - QS

     = 42 - 31 = 11 units

PS = PT - ST

     = 54 - 11

     = 43 units

PQ + QR = PR

12 + 14 = PR

PR = 26 units

RS + ST = RT

17 + 11 = RT

RT = 28 units

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